exp_final_two – Complete Experiment Report

two_attr_corr

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Vary_Correlation_with_high_Dimension (MvNormal, correlation, 30 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -7.369 1.17e-09 -1.660
HMC 0.3 1.754 0.0868 0.751
HMC 0.5 2.865 0.00672 1.383
HMC 0.9 4.598 6.68e-05 4.358
HMC 0.95 5.080 1.66e-05 4.675
HMC 0.99 4.735 4.88e-05 6.357
SMC 0.0 -0.990 0.327 -0.218
SMC 0.3 0.195 0.846 0.046
SMC 0.5 1.211 0.231 0.295
SMC 0.9 -0.326 0.746 -0.078
SMC 0.95 -0.002 0.998 -0.001
SMC 0.99 0.256 0.799 0.070
Metro 0.0 13.671 2.77e-18 4.711
Metro 0.3 6.518 2.79e-07 6.349
Metro 0.5 7.452 2.82e-08 12.659
Metro 0.9 6.108 1.17e-06 24.672
Metro 0.95 6.436 4.81e-07 37.101
Metro 0.99 7.139 7.37e-08 57.648
DEMetro_Z 0.0 46.026 1.15e-28 2226.429
DEMetro_Z 0.3 33.614 8.86e-25 1158.391
DEMetro_Z 0.5 47.380 4.98e-29 878.882
DEMetro_Z 0.9 49.351 1.51e-29 490.360
DEMetro_Z 0.95 47.348 4.99e-29 528.340
DEMetro_Z 0.99 35.011 2.75e-25 438.494
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 -46.074 1.12e-28 -8.412
HMC_vs_DEMetro_Z 0.3 -33.651 8.6e-25 -6.144
HMC_vs_DEMetro_Z 0.5 -47.168 5.72e-29 -8.612
HMC_vs_DEMetro_Z 0.9 -49.358 1.56e-29 -9.012
HMC_vs_DEMetro_Z 0.95 -46.986 6.39e-29 -8.578
HMC_vs_DEMetro_Z 0.99 -34.862 3.16e-25 -6.365
Metro_vs_SMC 0.0 15.586 1.24e-15 2.846
Metro_vs_SMC 0.3 6.514 3.93e-07 1.189
Metro_vs_SMC 0.5 7.052 9.31e-08 1.288
Metro_vs_SMC 0.9 6.218 8.77e-07 1.135
Metro_vs_SMC 0.95 6.450 4.67e-07 1.178
Metro_vs_SMC 0.99 7.132 7.54e-08 1.302
Metro_vs_DEMetro_Z 0.0 -45.976 1.19e-28 -8.394
Metro_vs_DEMetro_Z 0.3 -33.427 1.04e-24 -6.103
Metro_vs_DEMetro_Z 0.5 -47.737 4.05e-29 -8.716
Metro_vs_DEMetro_Z 0.9 -43.487 5.84e-28 -7.940
Metro_vs_DEMetro_Z 0.95 -44.215 3.64e-28 -8.072
Metro_vs_DEMetro_Z 0.99 -31.528 5.43e-24 -5.756
HMC_vs_Metro 0.0 -21.750 1.67e-19 -3.971
HMC_vs_Metro 0.3 -5.097 1.94e-05 -0.931
HMC_vs_Metro 0.5 -6.374 5.75e-07 -1.164
HMC_vs_Metro 0.9 -5.026 2.36e-05 -0.918
HMC_vs_Metro 0.95 -5.839 2.48e-06 -1.066
HMC_vs_Metro 0.99 -6.375 5.73e-07 -1.164
HMC_vs_SMC 0.0 -9.114 5.19e-10 -1.664
HMC_vs_SMC 0.3 1.795 0.0831 0.328
HMC_vs_SMC 0.5 2.356 0.0255 0.430
HMC_vs_SMC 0.9 4.652 6.66e-05 0.849
HMC_vs_SMC 0.95 4.873 3.62e-05 0.890
HMC_vs_SMC 0.99 4.547 8.92e-05 0.830
DEMetro_Z_vs_SMC 0.0 46.048 1.14e-28 8.407
DEMetro_Z_vs_SMC 0.3 33.633 8.73e-25 6.141
DEMetro_Z_vs_SMC 0.5 47.301 5.27e-29 8.636
DEMetro_Z_vs_SMC 0.9 49.180 1.73e-29 8.979
DEMetro_Z_vs_SMC 0.95 47.162 5.74e-29 8.611
DEMetro_Z_vs_SMC 0.99 34.959 2.92e-25 6.383
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.018 0.023 0.003 -1.660
HMC 0.3 0.027 0.023 0.006 0.751
HMC 0.5 0.031 0.021 0.008 1.383
HMC 0.9 0.078 0.019 0.013 4.358
HMC 0.95 0.076 0.020 0.012 4.675
HMC 0.99 0.110 0.019 0.014 6.357
SMC 0.0 0.022 0.023 0.003 -0.218
SMC 0.3 0.023 0.023 0.006 0.046
SMC 0.5 0.023 0.021 0.008 0.295
SMC 0.9 0.018 0.019 0.013 -0.078
SMC 0.95 0.020 0.020 0.012 -0.001
SMC 0.99 0.020 0.019 0.014 0.070
Metro 0.0 0.037 0.023 0.003 4.711
Metro 0.3 0.061 0.023 0.006 6.349
Metro 0.5 0.117 0.021 0.008 12.659
Metro 0.9 0.350 0.019 0.013 24.672
Metro 0.95 0.466 0.020 0.012 37.101
Metro 0.99 0.847 0.019 0.014 57.648
DEMetro_Z 0.0 6.576 0.023 0.003 2226.429
DEMetro_Z 0.3 6.941 0.023 0.006 1158.391
DEMetro_Z 0.5 6.672 0.021 0.008 878.882
DEMetro_Z 0.9 6.595 0.019 0.013 490.360
DEMetro_Z 0.95 6.374 0.020 0.012 528.340
DEMetro_Z 0.99 6.314 0.019 0.014 438.494
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 10.620 1.37e-14 3.406
HMC 0.3 6.242 9.36e-08 2.094
HMC 0.5 3.818 0.0004 1.401
HMC 0.9 5.564 4.93e-06 9.708
HMC 0.95 4.865 3.08e-05 4.462
HMC 0.99 5.080 1.79e-05 5.996
SMC 0.0 3.975 0.0002 1.097
SMC 0.3 2.121 0.0386 0.666
SMC 0.5 2.935 0.00508 1.013
SMC 0.9 2.191 0.0329 0.671
SMC 0.95 -2.311 0.0244 -0.584
SMC 0.99 0.322 0.749 0.080
Metro 0.0 14.655 2e-18 5.828
Metro 0.3 10.908 1.24e-12 7.100
Metro 0.5 7.803 1.1e-08 12.348
Metro 0.9 7.950 8.79e-09 29.149
Metro 0.95 6.115 1.16e-06 46.570
Metro 0.99 5.085 2e-05 82.884
DEMetro_Z 0.0 37.314 4.59e-26 48653.099
DEMetro_Z 0.3 31.375 6.22e-24 40102.407
DEMetro_Z 0.5 38.648 1.69e-26 34942.664
DEMetro_Z 0.9 40.390 4.81e-27 19605.728
DEMetro_Z 0.95 43.401 6.18e-28 9803.004
DEMetro_Z 0.99 33.324 1.13e-24 6898.138
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 6.884 1.46e-07 1.257
HMC_vs_SMC 0.3 3.828 0.000637 0.699
HMC_vs_SMC 0.5 0.782 0.441 0.143
HMC_vs_SMC 0.9 5.174 1.57e-05 0.945
HMC_vs_SMC 0.95 5.711 3.53e-06 1.043
HMC_vs_SMC 0.99 5.149 1.67e-05 0.940
Metro_vs_DEMetro_Z 0.0 -37.309 4.61e-26 -6.812
Metro_vs_DEMetro_Z 0.3 -31.370 6.25e-24 -5.727
Metro_vs_DEMetro_Z 0.5 -38.638 1.7e-26 -7.054
Metro_vs_DEMetro_Z 0.9 -40.299 5.13e-27 -7.358
Metro_vs_DEMetro_Z 0.95 -43.085 7.62e-28 -7.866
Metro_vs_DEMetro_Z 0.99 -32.105 3.25e-24 -5.862
HMC_vs_Metro 0.0 -6.018 1.52e-06 -1.099
HMC_vs_Metro 0.3 -7.690 1.77e-08 -1.404
HMC_vs_Metro 0.5 -6.791 1.87e-07 -1.240
HMC_vs_Metro 0.9 -4.416 0.000128 -0.806
HMC_vs_Metro 0.95 -5.623 4.5e-06 -1.027
HMC_vs_Metro 0.99 -4.628 7.13e-05 -0.845
HMC_vs_DEMetro_Z 0.0 -37.312 4.6e-26 -6.812
HMC_vs_DEMetro_Z 0.3 -31.373 6.23e-24 -5.728
HMC_vs_DEMetro_Z 0.5 -38.642 1.7e-26 -7.055
HMC_vs_DEMetro_Z 0.9 -40.387 4.82e-27 -7.374
HMC_vs_DEMetro_Z 0.95 -43.374 6.29e-28 -7.919
HMC_vs_DEMetro_Z 0.99 -33.315 1.14e-24 -6.082
Metro_vs_SMC 0.0 11.372 3.31e-12 2.076
Metro_vs_SMC 0.3 10.097 5.3e-11 1.843
Metro_vs_SMC 0.5 7.039 9.65e-08 1.285
Metro_vs_SMC 0.9 7.878 1.09e-08 1.438
Metro_vs_SMC 0.95 6.219 8.75e-07 1.135
Metro_vs_SMC 0.99 5.085 2.01e-05 0.928
DEMetro_Z_vs_SMC 0.0 37.315 4.59e-26 6.813
DEMetro_Z_vs_SMC 0.3 31.375 6.22e-24 5.728
DEMetro_Z_vs_SMC 0.5 38.646 1.69e-26 7.056
DEMetro_Z_vs_SMC 0.9 40.388 4.82e-27 7.374
DEMetro_Z_vs_SMC 0.95 43.398 6.19e-28 7.923
DEMetro_Z_vs_SMC 0.99 33.323 1.14e-24 6.084
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.044 0.032 0.004 3.406
HMC 0.3 0.040 0.031 0.004 2.094
HMC 0.5 0.037 0.030 0.005 1.401
HMC 0.9 0.114 0.024 0.009 9.708
HMC 0.95 0.110 0.035 0.017 4.462
HMC 0.99 0.161 0.031 0.022 5.996
SMC 0.0 0.035 0.032 0.004 1.097
SMC 0.3 0.034 0.031 0.004 0.666
SMC 0.5 0.035 0.030 0.005 1.013
SMC 0.9 0.030 0.024 0.009 0.671
SMC 0.95 0.025 0.035 0.017 -0.584
SMC 0.99 0.033 0.031 0.022 0.080
Metro 0.0 0.052 0.032 0.004 5.828
Metro 0.3 0.062 0.031 0.004 7.100
Metro 0.5 0.095 0.030 0.005 12.348
Metro 0.9 0.294 0.024 0.009 29.149
Metro 0.95 0.826 0.035 0.017 46.570
Metro 0.99 1.818 0.031 0.022 82.884
DEMetro_Z 0.0 172.552 0.032 0.004 48653.099
DEMetro_Z 0.3 173.314 0.031 0.004 40102.407
DEMetro_Z 0.5 183.257 0.030 0.005 34942.664
DEMetro_Z 0.9 181.976 0.024 0.009 19605.728
DEMetro_Z 0.95 166.644 0.035 0.017 9803.004
DEMetro_Z 0.99 148.704 0.031 0.022 6898.138
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -2.243 0.0293 -0.493
HMC 0.3 2.788 0.00807 1.257
HMC 0.5 3.807 0.000514 1.983
HMC 0.9 6.888 1.12e-07 8.147
HMC 0.95 7.657 1.21e-08 7.463
HMC 0.99 7.836 1.02e-08 12.910
SMC 0.0 -0.319 0.751 -0.074
SMC 0.3 0.844 0.402 0.199
SMC 0.5 1.902 0.0624 0.446
SMC 0.9 0.022 0.983 0.005
SMC 0.95 -0.730 0.468 -0.179
SMC 0.99 0.553 0.582 0.156
Metro 0.0 16.267 7.65e-21 5.908
Metro 0.3 7.104 6.37e-08 8.852
Metro 0.5 8.318 3.2e-09 17.506
Metro 0.9 7.861 1.12e-08 40.384
Metro 0.95 10.272 3.5e-11 62.374
Metro 0.99 10.820 1.06e-11 111.561
DEMetro_Z 0.0 68.464 1.27e-33 6006.686
DEMetro_Z 0.3 66.806 2.58e-33 3123.408
DEMetro_Z 0.5 82.888 5.1e-36 2450.645
DEMetro_Z 0.9 95.546 8.26e-38 1423.052
DEMetro_Z 0.95 102.759 1e-38 1366.570
DEMetro_Z 0.99 63.071 1.34e-32 1234.892
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 -68.439 1.29e-33 -12.495
Metro_vs_DEMetro_Z 0.3 -66.497 2.96e-33 -12.141
Metro_vs_DEMetro_Z 0.5 -82.494 5.88e-36 -15.061
Metro_vs_DEMetro_Z 0.9 -87.275 1.16e-36 -15.934
Metro_vs_DEMetro_Z 0.95 -84.548 2.89e-36 -15.436
Metro_vs_DEMetro_Z 0.99 -48.540 2.51e-29 -8.862
DEMetro_Z_vs_SMC 0.0 68.497 1.26e-33 12.506
DEMetro_Z_vs_SMC 0.3 66.811 2.58e-33 12.198
DEMetro_Z_vs_SMC 0.5 82.857 5.18e-36 15.128
DEMetro_Z_vs_SMC 0.9 95.461 8.66e-38 17.429
DEMetro_Z_vs_SMC 0.95 102.510 1.1e-38 18.716
DEMetro_Z_vs_SMC 0.99 63.229 1.26e-32 11.544
HMC_vs_DEMetro_Z 0.0 -68.479 1.27e-33 -12.502
HMC_vs_DEMetro_Z 0.3 -66.940 2.44e-33 -12.222
HMC_vs_DEMetro_Z 0.5 -82.770 5.34e-36 -15.112
HMC_vs_DEMetro_Z 0.9 -94.464 1.17e-37 -17.247
HMC_vs_DEMetro_Z 0.95 -101.743 1.37e-38 -18.576
HMC_vs_DEMetro_Z 0.99 -62.974 1.42e-32 -11.497
HMC_vs_Metro 0.0 -20.735 6.16e-19 -3.786
HMC_vs_Metro 0.3 -5.540 5.66e-06 -1.012
HMC_vs_Metro 0.5 -7.118 7.83e-08 -1.300
HMC_vs_Metro 0.9 -6.258 7.87e-07 -1.143
HMC_vs_Metro 0.95 -9.279 3.51e-10 -1.694
HMC_vs_Metro 0.99 -9.614 1.6e-10 -1.755
HMC_vs_SMC 0.0 -2.694 0.0116 -0.492
HMC_vs_SMC 0.3 2.692 0.0117 0.491
HMC_vs_SMC 0.5 3.080 0.0045 0.562
HMC_vs_SMC 0.9 6.672 2.56e-07 1.218
HMC_vs_SMC 0.95 7.583 2.33e-08 1.384
HMC_vs_SMC 0.99 7.728 1.6e-08 1.411
Metro_vs_SMC 0.0 17.126 1.05e-16 3.127
Metro_vs_SMC 0.3 6.994 1.09e-07 1.277
Metro_vs_SMC 0.5 7.974 8.56e-09 1.456
Metro_vs_SMC 0.9 7.969 8.67e-09 1.455
Metro_vs_SMC 0.95 10.391 2.74e-11 1.897
Metro_vs_SMC 0.99 10.806 1.11e-11 1.973
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.028 0.029 0.002 -0.493
HMC 0.3 0.033 0.029 0.003 1.257
HMC 0.5 0.036 0.027 0.004 1.983
HMC 0.9 0.085 0.024 0.007 8.147
HMC 0.95 0.081 0.025 0.007 7.463
HMC 0.99 0.125 0.024 0.008 12.910
SMC 0.0 0.029 0.029 0.002 -0.074
SMC 0.3 0.029 0.029 0.003 0.199
SMC 0.5 0.029 0.027 0.004 0.446
SMC 0.9 0.024 0.024 0.007 0.005
SMC 0.95 0.024 0.025 0.007 -0.179
SMC 0.99 0.026 0.024 0.008 0.156
Metro 0.0 0.039 0.029 0.002 5.908
Metro 0.3 0.058 0.029 0.003 8.852
Metro 0.5 0.103 0.027 0.004 17.506
Metro 0.9 0.324 0.024 0.007 40.384
Metro 0.95 0.489 0.025 0.007 62.374
Metro 0.99 0.895 0.024 0.008 111.561
DEMetro_Z 0.0 10.319 0.029 0.002 6006.686
DEMetro_Z 0.3 10.414 0.029 0.003 3123.408
DEMetro_Z 0.5 10.599 0.027 0.004 2450.645
DEMetro_Z 0.9 10.585 0.024 0.007 1423.052
DEMetro_Z 0.95 10.185 0.025 0.007 1366.570
DEMetro_Z 0.99 9.665 0.024 0.008 1234.892
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -3.311 0.0018 -0.698
HMC 0.3 2.644 0.0117 1.226
HMC 0.5 3.833 0.000478 2.024
HMC 0.9 7.985 5.56e-09 8.733
HMC 0.95 9.274 1.14e-10 6.939
HMC 0.99 7.750 1.13e-08 9.691
SMC 0.0 0.520 0.605 0.116
SMC 0.3 0.731 0.468 0.171
SMC 0.5 2.630 0.0109 0.681
SMC 0.9 0.354 0.725 0.088
SMC 0.95 -1.085 0.282 -0.258
SMC 0.99 0.317 0.752 0.084
Metro 0.0 14.385 6.1e-20 4.462
Metro 0.3 8.134 3.65e-09 8.565
Metro 0.5 9.203 3.58e-10 18.251
Metro 0.9 9.087 5.37e-10 40.878
Metro 0.95 13.104 9.8e-14 56.464
Metro 0.99 13.453 5.11e-14 63.382
DEMetro_Z 0.0 79.554 1.31e-35 332.840
DEMetro_Z 0.3 74.843 6.28e-35 230.100
DEMetro_Z 0.5 117.631 3.58e-41 200.432
DEMetro_Z 0.9 107.474 4.54e-41 117.901
DEMetro_Z 0.95 76.826 4.25e-36 102.910
DEMetro_Z 0.99 86.147 2.3e-38 88.580
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 79.145 1.95e-35 14.450
DEMetro_Z_vs_SMC 0.3 75.388 7.93e-35 13.764
DEMetro_Z_vs_SMC 0.5 114.299 4.73e-40 20.868
DEMetro_Z_vs_SMC 0.9 107.595 2.72e-39 19.644
DEMetro_Z_vs_SMC 0.95 76.657 4.9e-35 13.996
DEMetro_Z_vs_SMC 0.99 86.922 1.3e-36 15.870
HMC_vs_Metro 0.0 -20.927 4.79e-19 -3.821
HMC_vs_Metro 0.3 -6.045 1.41e-06 -1.104
HMC_vs_Metro 0.5 -7.921 9.78e-09 -1.446
HMC_vs_Metro 0.9 -7.117 7.85e-08 -1.299
HMC_vs_Metro 0.95 -11.544 2.31e-12 -2.108
HMC_vs_Metro 0.99 -11.651 1.85e-12 -2.127
Metro_vs_DEMetro_Z 0.0 -78.332 2.62e-35 -14.301
Metro_vs_DEMetro_Z 0.3 -66.519 2.93e-33 -12.145
Metro_vs_DEMetro_Z 0.5 -71.438 3.74e-34 -13.043
Metro_vs_DEMetro_Z 0.9 -17.030 1.22e-16 -3.109
Metro_vs_DEMetro_Z 0.95 -10.758 1.23e-11 -1.964
Metro_vs_DEMetro_Z 0.99 -5.307 1.08e-05 -0.969
HMC_vs_SMC 0.0 -4.530 9.36e-05 -0.827
HMC_vs_SMC 0.3 2.611 0.0141 0.477
HMC_vs_SMC 0.5 2.577 0.0153 0.470
HMC_vs_SMC 0.9 7.669 1.87e-08 1.400
HMC_vs_SMC 0.95 9.491 2.13e-10 1.733
HMC_vs_SMC 0.99 7.702 1.71e-08 1.406
Metro_vs_SMC 0.0 15.126 2.7e-15 2.762
Metro_vs_SMC 0.3 8.029 7.45e-09 1.466
Metro_vs_SMC 0.5 8.850 9.77e-10 1.616
Metro_vs_SMC 0.9 9.191 4.32e-10 1.678
Metro_vs_SMC 0.95 13.347 6.55e-14 2.437
Metro_vs_SMC 0.99 13.507 4.86e-14 2.466
HMC_vs_DEMetro_Z 0.0 -79.370 1.79e-35 -14.491
HMC_vs_DEMetro_Z 0.3 -73.321 1.77e-34 -13.386
HMC_vs_DEMetro_Z 0.5 -106.914 3.27e-39 -19.520
HMC_vs_DEMetro_Z 0.9 -72.689 2.27e-34 -13.271
HMC_vs_DEMetro_Z 0.95 -59.078 8.91e-32 -10.786
HMC_vs_DEMetro_Z 0.99 -58.006 1.51e-31 -10.590
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.013 0.014 0.002 -0.698
HMC 0.3 0.018 0.015 0.002 1.226
HMC 0.5 0.020 0.014 0.003 2.024
HMC 0.9 0.055 0.014 0.005 8.733
HMC 0.95 0.052 0.015 0.005 6.939
HMC 0.99 0.076 0.014 0.006 9.691
SMC 0.0 0.015 0.014 0.002 0.116
SMC 0.3 0.015 0.015 0.002 0.171
SMC 0.5 0.016 0.014 0.003 0.681
SMC 0.9 0.014 0.014 0.005 0.088
SMC 0.95 0.013 0.015 0.005 -0.258
SMC 0.99 0.015 0.014 0.006 0.084
Metro 0.0 0.022 0.014 0.002 4.462
Metro 0.3 0.036 0.015 0.002 8.565
Metro 0.5 0.065 0.014 0.003 18.251
Metro 0.9 0.209 0.014 0.005 40.878
Metro 0.95 0.320 0.015 0.005 56.464
Metro 0.99 0.416 0.014 0.006 63.382
DEMetro_Z 0.0 0.580 0.014 0.002 332.840
DEMetro_Z 0.3 0.585 0.015 0.002 230.100
DEMetro_Z 0.5 0.573 0.014 0.003 200.432
DEMetro_Z 0.9 0.576 0.014 0.005 117.901
DEMetro_Z 0.95 0.571 0.015 0.005 102.910
DEMetro_Z 0.99 0.576 0.014 0.006 88.580
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -6.417 2.98e-08 -1.551
HMC 0.3 2.029 0.0484 0.767
HMC 0.5 5.121 7.24e-06 2.151
HMC 0.9 4.049 0.000315 3.806
HMC 0.95 5.937 1.49e-06 6.118
HMC 0.99 5.237 1.19e-05 7.371
SMC 0.0 -1.153 0.254 -0.288
SMC 0.3 -0.233 0.816 -0.062
SMC 0.5 2.022 0.0485 0.654
SMC 0.9 1.039 0.303 0.285
SMC 0.95 0.317 0.752 0.087
SMC 0.99 -1.030 0.307 -0.250
Metro 0.0 13.995 7.35e-19 4.705
Metro 0.3 7.268 4.27e-08 9.981
Metro 0.5 7.327 3.93e-08 12.434
Metro 0.9 6.108 1.17e-06 25.587
Metro 0.95 7.803 1.31e-08 69.684
Metro 0.99 6.469 4.43e-07 86.237
DEMetro_Z 0.0 26.418 7.74e-22 3876.685
DEMetro_Z 0.3 28.650 8.01e-23 2005.937
DEMetro_Z 0.5 35.936 1.33e-25 1538.703
DEMetro_Z 0.9 46.667 7.69e-29 873.192
DEMetro_Z 0.95 36.580 8.03e-26 857.782
DEMetro_Z 0.99 29.061 5.35e-23 719.048
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 -26.423 7.7e-22 -4.824
HMC_vs_DEMetro_Z 0.3 -28.688 7.72e-23 -5.238
HMC_vs_DEMetro_Z 0.5 -35.861 1.42e-25 -6.547
HMC_vs_DEMetro_Z 0.9 -47.014 6.28e-29 -8.583
HMC_vs_DEMetro_Z 0.95 -36.439 9.01e-26 -6.653
HMC_vs_DEMetro_Z 0.99 -28.539 8.93e-23 -5.210
Metro_vs_SMC 0.0 14.850 4.35e-15 2.711
Metro_vs_SMC 0.3 7.047 9.45e-08 1.287
Metro_vs_SMC 0.5 7.343 4.34e-08 1.341
Metro_vs_SMC 0.9 6.006 1.57e-06 1.096
Metro_vs_SMC 0.95 7.792 1.36e-08 1.423
Metro_vs_SMC 0.99 6.468 4.46e-07 1.181
Metro_vs_DEMetro_Z 0.0 -26.384 8.02e-22 -4.817
Metro_vs_DEMetro_Z 0.3 -28.585 8.53e-23 -5.219
Metro_vs_DEMetro_Z 0.5 -35.836 1.45e-25 -6.543
Metro_vs_DEMetro_Z 0.9 -43.959 4.29e-28 -8.026
Metro_vs_DEMetro_Z 0.95 -30.644 1.21e-23 -5.595
Metro_vs_DEMetro_Z 0.99 -20.604 7.32e-19 -3.762
HMC_vs_Metro 0.0 -18.028 2.68e-17 -3.292
HMC_vs_Metro 0.3 -6.749 2.09e-07 -1.232
HMC_vs_Metro 0.5 -5.906 2.06e-06 -1.078
HMC_vs_Metro 0.9 -5.095 1.95e-05 -0.930
HMC_vs_Metro 0.95 -7.155 7.1e-08 -1.306
HMC_vs_Metro 0.99 -5.863 2.32e-06 -1.070
HMC_vs_SMC 0.0 -6.255 7.93e-07 -1.142
HMC_vs_SMC 0.3 2.220 0.0344 0.405
HMC_vs_SMC 0.5 3.027 0.00515 0.553
HMC_vs_SMC 0.9 3.828 0.000636 0.699
HMC_vs_SMC 0.95 5.949 1.83e-06 1.086
HMC_vs_SMC 0.99 5.396 8.45e-06 0.985
DEMetro_Z_vs_SMC 0.0 26.426 7.67e-22 4.825
DEMetro_Z_vs_SMC 0.3 28.643 8.06e-23 5.229
DEMetro_Z_vs_SMC 0.5 35.924 1.35e-25 6.559
DEMetro_Z_vs_SMC 0.9 46.733 7.45e-29 8.532
DEMetro_Z_vs_SMC 0.95 36.717 7.26e-26 6.704
DEMetro_Z_vs_SMC 0.99 29.099 5.18e-23 5.313
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.019 0.023 0.003 -1.551
HMC 0.3 0.027 0.023 0.006 0.767
HMC 0.5 0.037 0.021 0.008 2.151
HMC 0.9 0.070 0.019 0.013 3.806
HMC 0.95 0.093 0.020 0.012 6.118
HMC 0.99 0.125 0.019 0.014 7.371
SMC 0.0 0.022 0.023 0.003 -0.288
SMC 0.3 0.022 0.023 0.006 -0.062
SMC 0.5 0.026 0.021 0.008 0.654
SMC 0.9 0.023 0.019 0.013 0.285
SMC 0.95 0.021 0.020 0.012 0.087
SMC 0.99 0.015 0.019 0.014 -0.250
Metro 0.0 0.037 0.023 0.003 4.705
Metro 0.3 0.082 0.023 0.006 9.981
Metro 0.5 0.115 0.021 0.008 12.434
Metro 0.9 0.362 0.019 0.013 25.587
Metro 0.95 0.858 0.020 0.012 69.684
Metro 0.99 1.257 0.019 0.014 86.237
DEMetro_Z 0.0 11.433 0.023 0.003 3876.685
DEMetro_Z 0.3 12.004 0.023 0.006 2005.937
DEMetro_Z 0.5 11.665 0.021 0.008 1538.703
DEMetro_Z 0.9 11.729 0.019 0.013 873.192
DEMetro_Z 0.95 10.336 0.020 0.012 857.782
DEMetro_Z 0.99 10.341 0.019 0.014 719.048
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 9.358 1.76e-12 3.200
HMC 0.3 4.236 9.65e-05 1.399
HMC 0.5 3.475 0.00137 2.028
HMC 0.9 6.029 1.12e-06 5.962
HMC 0.95 6.055 1.03e-06 5.819
HMC 0.99 4.739 4.64e-05 5.156
SMC 0.0 -0.446 0.657 -0.137
SMC 0.3 0.654 0.515 0.176
SMC 0.5 0.758 0.452 0.189
SMC 0.9 2.212 0.0318 0.785
SMC 0.95 -2.560 0.0131 -0.625
SMC 0.99 0.024 0.981 0.007
Metro 0.0 17.071 1.45e-22 5.654
Metro 0.3 11.352 2.55e-13 6.625
Metro 0.5 7.865 9.19e-09 11.856
Metro 0.9 7.533 2.57e-08 28.417
Metro 0.95 7.472 3.01e-08 27.659
Metro 0.99 32.793 2.29e-25 37.266
DEMetro_Z 0.0 15.610 1.2e-15 6200.205
DEMetro_Z 0.3 11.577 2.16e-12 4716.960
DEMetro_Z 0.5 15.263 2.14e-15 3597.057
DEMetro_Z 0.9 14.765 5.04e-15 2155.139
DEMetro_Z 0.95 14.166 1.46e-14 1151.047
DEMetro_Z 0.99 12.562 2.96e-13 1024.418
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 8.834 1.02e-09 1.613
HMC_vs_SMC 0.3 4.144 0.00027 0.757
HMC_vs_SMC 0.5 3.350 0.00226 0.612
HMC_vs_SMC 0.9 4.786 4.6e-05 0.874
HMC_vs_SMC 0.95 6.494 4.15e-07 1.186
HMC_vs_SMC 0.99 4.477 0.000108 0.817
Metro_vs_DEMetro_Z 0.0 -15.598 1.22e-15 -2.848
Metro_vs_DEMetro_Z 0.3 -11.566 2.21e-12 -2.112
Metro_vs_DEMetro_Z 0.5 -15.218 2.32e-15 -2.778
Metro_vs_DEMetro_Z 0.9 -14.512 7.86e-15 -2.649
Metro_vs_DEMetro_Z 0.95 -13.878 2.45e-14 -2.534
Metro_vs_DEMetro_Z 0.99 -12.151 6.68e-13 -2.219
HMC_vs_Metro 0.0 -5.282 1.16e-05 -0.964
HMC_vs_Metro 0.3 -9.565 1.79e-10 -1.746
HMC_vs_Metro 0.5 -5.814 2.66e-06 -1.062
HMC_vs_Metro 0.9 -5.528 5.86e-06 -1.009
HMC_vs_Metro 0.95 -5.803 2.74e-06 -1.059
HMC_vs_Metro 0.99 -20.006 1.63e-18 -3.653
HMC_vs_DEMetro_Z 0.0 -15.602 1.21e-15 -2.848
HMC_vs_DEMetro_Z 0.3 -11.573 2.17e-12 -2.113
HMC_vs_DEMetro_Z 0.5 -15.257 2.17e-15 -2.786
HMC_vs_DEMetro_Z 0.9 -14.724 5.42e-15 -2.688
HMC_vs_DEMetro_Z 0.95 -14.078 1.7e-14 -2.570
HMC_vs_DEMetro_Z 0.99 -12.480 3.47e-13 -2.279
Metro_vs_SMC 0.0 14.953 3.64e-15 2.730
Metro_vs_SMC 0.3 10.842 1.02e-11 1.979
Metro_vs_SMC 0.5 7.608 2.18e-08 1.389
Metro_vs_SMC 0.9 7.216 6.05e-08 1.318
Metro_vs_SMC 0.95 7.683 1.8e-08 1.403
Metro_vs_SMC 0.99 30.184 1.85e-23 5.511
DEMetro_Z_vs_SMC 0.0 15.606 1.2e-15 2.849
DEMetro_Z_vs_SMC 0.3 11.576 2.16e-12 2.114
DEMetro_Z_vs_SMC 0.5 15.265 2.14e-15 2.787
DEMetro_Z_vs_SMC 0.9 14.757 5.11e-15 2.694
DEMetro_Z_vs_SMC 0.95 14.177 1.43e-14 2.588
DEMetro_Z_vs_SMC 0.99 12.558 2.98e-13 2.293
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.043 0.032 0.004 3.200
HMC 0.3 0.037 0.031 0.004 1.399
HMC 0.5 0.041 0.030 0.005 2.028
HMC 0.9 0.079 0.024 0.009 5.962
HMC 0.95 0.133 0.035 0.017 5.819
HMC 0.99 0.143 0.031 0.022 5.156
SMC 0.0 0.031 0.032 0.004 -0.137
SMC 0.3 0.032 0.031 0.004 0.176
SMC 0.5 0.031 0.030 0.005 0.189
SMC 0.9 0.031 0.024 0.009 0.785
SMC 0.95 0.024 0.035 0.017 -0.625
SMC 0.99 0.032 0.031 0.022 0.007
Metro 0.0 0.052 0.032 0.004 5.654
Metro 0.3 0.060 0.031 0.004 6.625
Metro 0.5 0.092 0.030 0.005 11.856
Metro 0.9 0.287 0.024 0.009 28.417
Metro 0.95 0.505 0.035 0.017 27.659
Metro 0.99 0.835 0.031 0.022 37.266
DEMetro_Z 0.0 22.017 0.032 0.004 6200.205
DEMetro_Z 0.3 20.413 0.031 0.004 4716.960
DEMetro_Z 0.5 18.892 0.030 0.005 3597.057
DEMetro_Z 0.9 20.025 0.024 0.009 2155.139
DEMetro_Z 0.95 19.597 0.035 0.017 1151.047
DEMetro_Z 0.99 22.110 0.031 0.022 1024.418
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -2.031 0.0472 -0.465
HMC 0.3 3.100 0.00339 1.237
HMC 0.5 5.788 9.87e-07 2.671
HMC 0.9 5.552 4.7e-06 6.608
HMC 0.95 9.272 2.16e-10 10.438
HMC 0.99 6.841 1.49e-07 13.355
SMC 0.0 -1.686 0.0972 -0.412
SMC 0.3 -0.221 0.826 -0.063
SMC 0.5 1.980 0.0534 0.699
SMC 0.9 1.734 0.0883 0.471
SMC 0.95 0.135 0.893 0.035
SMC 0.99 -0.285 0.777 -0.075
Metro 0.0 15.741 5.59e-20 5.930
Metro 0.3 7.237 5.11e-08 13.457
Metro 0.5 8.212 4.2e-09 17.431
Metro 0.9 7.666 1.85e-08 41.923
Metro 0.95 8.676 1.48e-09 94.176
Metro 0.99 7.309 4.73e-08 136.833
DEMetro_Z 0.0 26.009 1.19e-21 5552.249
DEMetro_Z 0.3 30.287 1.68e-23 2965.179
DEMetro_Z 0.5 41.006 3.12e-27 2212.991
DEMetro_Z 0.9 43.781 4.8e-28 1299.595
DEMetro_Z 0.95 37.706 3.4e-26 1154.947
DEMetro_Z 0.99 30.894 9.59e-24 1101.955
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 -25.977 1.24e-21 -4.743
Metro_vs_DEMetro_Z 0.3 -30.228 1.78e-23 -5.519
Metro_vs_DEMetro_Z 0.5 -41.042 3.05e-27 -7.493
Metro_vs_DEMetro_Z 0.9 -41.075 2.98e-27 -7.499
Metro_vs_DEMetro_Z 0.95 -31.639 4.91e-24 -5.776
Metro_vs_DEMetro_Z 0.99 -21.880 1.42e-19 -3.995
DEMetro_Z_vs_SMC 0.0 26.018 1.18e-21 4.750
DEMetro_Z_vs_SMC 0.3 30.288 1.68e-23 5.530
DEMetro_Z_vs_SMC 0.5 41.023 3.09e-27 7.490
DEMetro_Z_vs_SMC 0.9 43.781 4.82e-28 7.993
DEMetro_Z_vs_SMC 0.95 37.768 3.25e-26 6.895
DEMetro_Z_vs_SMC 0.99 30.929 9.31e-24 5.647
HMC_vs_DEMetro_Z 0.0 -26.004 1.2e-21 -4.748
HMC_vs_DEMetro_Z 0.3 -30.299 1.66e-23 -5.532
HMC_vs_DEMetro_Z 0.5 -40.940 3.27e-27 -7.475
HMC_vs_DEMetro_Z 0.9 -44.078 3.97e-28 -8.047
HMC_vs_DEMetro_Z 0.95 -37.353 4.46e-26 -6.820
HMC_vs_DEMetro_Z 0.99 -30.400 1.51e-23 -5.550
HMC_vs_Metro 0.0 -17.449 6.4e-17 -3.186
HMC_vs_Metro 0.3 -6.635 2.84e-07 -1.211
HMC_vs_Metro 0.5 -6.680 2.52e-07 -1.220
HMC_vs_Metro 0.9 -6.344 6.22e-07 -1.158
HMC_vs_Metro 0.95 -7.657 1.92e-08 -1.398
HMC_vs_Metro 0.99 -6.530 3.76e-07 -1.192
HMC_vs_SMC 0.0 -0.295 0.77 -0.054
HMC_vs_SMC 0.3 3.125 0.00401 0.571
HMC_vs_SMC 0.5 3.583 0.00123 0.654
HMC_vs_SMC 0.9 5.237 1.31e-05 0.956
HMC_vs_SMC 0.95 9.441 2.39e-10 1.724
HMC_vs_SMC 0.99 6.812 1.76e-07 1.244
Metro_vs_SMC 0.0 17.267 8.45e-17 3.152
Metro_vs_SMC 0.3 7.069 8.92e-08 1.291
Metro_vs_SMC 0.5 8.341 3.41e-09 1.523
Metro_vs_SMC 0.9 7.601 2.22e-08 1.388
Metro_vs_SMC 0.95 8.670 1.52e-09 1.583
Metro_vs_SMC 0.99 7.292 4.96e-08 1.331
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.029 0.029 0.002 -0.465
HMC 0.3 0.033 0.029 0.003 1.237
HMC 0.5 0.039 0.027 0.004 2.671
HMC 0.9 0.073 0.024 0.007 6.608
HMC 0.95 0.103 0.025 0.007 10.438
HMC 0.99 0.129 0.024 0.008 13.355
SMC 0.0 0.029 0.029 0.002 -0.412
SMC 0.3 0.029 0.029 0.003 -0.063
SMC 0.5 0.030 0.027 0.004 0.699
SMC 0.9 0.028 0.024 0.007 0.471
SMC 0.95 0.025 0.025 0.007 0.035
SMC 0.99 0.024 0.024 0.008 -0.075
Metro 0.0 0.039 0.029 0.002 5.930
Metro 0.3 0.074 0.029 0.003 13.457
Metro 0.5 0.102 0.027 0.004 17.431
Metro 0.9 0.335 0.024 0.007 41.923
Metro 0.95 0.725 0.025 0.007 94.176
Metro 0.99 1.093 0.024 0.008 136.833
DEMetro_Z 0.0 9.540 0.029 0.002 5552.249
DEMetro_Z 0.3 9.888 0.029 0.003 2965.179
DEMetro_Z 0.5 9.574 0.027 0.004 2212.991
DEMetro_Z 0.9 9.669 0.024 0.007 1299.595
DEMetro_Z 0.95 8.612 0.025 0.007 1154.947
DEMetro_Z 0.99 8.628 0.024 0.008 1101.955
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -2.575 0.0132 -0.550
HMC 0.3 2.780 0.00807 1.151
HMC 0.5 5.362 4.57e-06 2.777
HMC 0.9 6.444 3.61e-07 6.819
HMC 0.95 8.717 8.75e-10 9.963
HMC 0.99 6.354 5.45e-07 10.641
SMC 0.0 -1.287 0.203 -0.315
SMC 0.3 -0.128 0.899 -0.036
SMC 0.5 2.359 0.0225 0.836
SMC 0.9 2.104 0.0399 0.590
SMC 0.95 0.045 0.964 0.012
SMC 0.99 -0.401 0.69 -0.102
Metro 0.0 13.931 3.2e-19 4.404
Metro 0.3 7.606 1.84e-08 11.985
Metro 0.5 8.990 5.99e-10 17.806
Metro 0.9 9.588 1.64e-10 41.564
Metro 0.95 11.658 1.78e-12 76.503
Metro 0.99 16.229 4.2e-16 109.348
DEMetro_Z 0.0 78.194 2.53e-35 547.518
DEMetro_Z 0.3 80.435 1e-35 375.008
DEMetro_Z 0.5 58.947 8.44e-32 329.757
DEMetro_Z 0.9 78.125 1.46e-35 198.418
DEMetro_Z 0.95 124.903 2.38e-42 172.828
DEMetro_Z 0.99 97.253 5.76e-39 143.415
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 78.813 2.2e-35 14.389
DEMetro_Z_vs_SMC 0.3 80.340 1.26e-35 14.668
DEMetro_Z_vs_SMC 0.5 59.418 7.56e-32 10.848
DEMetro_Z_vs_SMC 0.9 76.538 5.12e-35 13.974
DEMetro_Z_vs_SMC 0.95 119.499 1.31e-40 21.817
DEMetro_Z_vs_SMC 0.99 97.911 4.16e-38 17.876
HMC_vs_Metro 0.0 -16.354 3.54e-16 -2.986
HMC_vs_Metro 0.3 -6.987 1.11e-07 -1.276
HMC_vs_Metro 0.5 -7.320 4.61e-08 -1.336
HMC_vs_Metro 0.9 -7.982 8.38e-09 -1.457
HMC_vs_Metro 0.95 -9.732 1.22e-10 -1.777
HMC_vs_Metro 0.99 -14.150 1.5e-14 -2.583
Metro_vs_DEMetro_Z 0.0 -77.249 3.92e-35 -14.104
Metro_vs_DEMetro_Z 0.3 -69.684 7.67e-34 -12.723
Metro_vs_DEMetro_Z 0.5 -57.918 1.58e-31 -10.574
Metro_vs_DEMetro_Z 0.9 -30.150 1.91e-23 -5.505
Metro_vs_DEMetro_Z 0.95 -14.204 1.36e-14 -2.593
Metro_vs_DEMetro_Z 0.99 -4.842 3.94e-05 -0.884
HMC_vs_SMC 0.0 -1.453 0.157 -0.265
HMC_vs_SMC 0.3 2.756 0.01 0.503
HMC_vs_SMC 0.5 3.303 0.00255 0.603
HMC_vs_SMC 0.9 5.881 2.21e-06 1.074
HMC_vs_SMC 0.95 9.206 4.17e-10 1.681
HMC_vs_SMC 0.99 6.356 6.03e-07 1.160
Metro_vs_SMC 0.0 14.838 4.45e-15 2.709
Metro_vs_SMC 0.3 7.335 4.43e-08 1.339
Metro_vs_SMC 0.5 8.997 6.87e-10 1.643
Metro_vs_SMC 0.9 9.614 1.6e-10 1.755
Metro_vs_SMC 0.95 11.624 1.95e-12 2.122
Metro_vs_SMC 0.99 16.172 4.75e-16 2.953
HMC_vs_DEMetro_Z 0.0 -78.435 2.53e-35 -14.320
HMC_vs_DEMetro_Z 0.3 -80.472 1.2e-35 -14.692
HMC_vs_DEMetro_Z 0.5 -57.207 2.25e-31 -10.444
HMC_vs_DEMetro_Z 0.9 -66.275 3.25e-33 -12.100
HMC_vs_DEMetro_Z 0.95 -90.003 4.75e-37 -16.432
HMC_vs_DEMetro_Z 0.99 -58.500 1.18e-31 -10.681
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.013 0.014 0.002 -0.550
HMC 0.3 0.017 0.015 0.002 1.151
HMC 0.5 0.022 0.014 0.003 2.777
HMC 0.9 0.046 0.014 0.005 6.819
HMC 0.95 0.069 0.015 0.005 9.963
HMC 0.99 0.082 0.014 0.006 10.641
SMC 0.0 0.014 0.014 0.002 -0.315
SMC 0.3 0.014 0.015 0.002 -0.036
SMC 0.5 0.016 0.014 0.003 0.836
SMC 0.9 0.016 0.014 0.005 0.590
SMC 0.95 0.015 0.015 0.005 0.012
SMC 0.99 0.014 0.014 0.006 -0.102
Metro 0.0 0.022 0.014 0.002 4.404
Metro 0.3 0.044 0.015 0.002 11.985
Metro 0.5 0.064 0.014 0.003 17.806
Metro 0.9 0.212 0.014 0.005 41.564
Metro 0.95 0.428 0.015 0.005 76.503
Metro 0.99 0.708 0.014 0.006 109.348
DEMetro_Z 0.0 0.945 0.014 0.002 547.518
DEMetro_Z 0.3 0.944 0.015 0.002 375.008
DEMetro_Z 0.5 0.933 0.014 0.003 329.757
DEMetro_Z 0.9 0.960 0.014 0.005 198.418
DEMetro_Z 0.95 0.948 0.015 0.005 172.828
DEMetro_Z 0.99 0.924 0.014 0.006 143.415
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Forest & Ridge Plots
Pooled
0.0 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.9 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.95 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.99 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
0.0 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.9 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.95 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.99 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
0.0
0.3
0.5
0.9
0.95
0.99
Chain
0.0
0.3
0.5
0.9
0.95
0.99

Vary_Correlation_with_heavy_Tails (MvStudentT, correlation, 30 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -0.044 0.965 -0.012
HMC 0.3 2.068 0.0439 0.709
HMC 0.5 1.719 0.0912 0.513
HMC 0.9 3.252 0.00242 1.631
HMC 0.95 3.565 0.000957 1.591
HMC 0.99 2.277 0.0274 0.815
SMC 0.0 -0.826 0.413 -0.186
SMC 0.3 -0.590 0.558 -0.130
SMC 0.5 0.160 0.874 0.040
SMC 0.9 1.043 0.302 0.324
SMC 0.95 0.493 0.624 0.114
SMC 0.99 -0.084 0.934 -0.027
Metro 0.0 1.882 0.0673 0.886
Metro 0.3 3.754 0.000632 2.220
Metro 0.5 2.602 0.0128 1.095
Metro 0.9 1.789 0.0841 16.066
Metro 0.95 4.192 0.000232 9.673
Metro 0.99 4.511 9.82e-05 28.951
DEMetro_Z 0.0 3.308 0.00202 1.537
DEMetro_Z 0.3 3.426 0.00153 1.815
DEMetro_Z 0.5 3.894 0.000315 1.426
DEMetro_Z 0.9 3.525 0.00133 3.339
DEMetro_Z 0.95 4.279 0.000125 2.175
DEMetro_Z 0.99 3.622 0.00101 3.089
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 -3.266 0.0028 -0.596
HMC_vs_DEMetro_Z 0.3 -2.234 0.0334 -0.408
HMC_vs_DEMetro_Z 0.5 -2.340 0.0264 -0.427
HMC_vs_DEMetro_Z 0.9 -1.661 0.108 -0.303
HMC_vs_DEMetro_Z 0.95 -0.953 0.348 -0.174
HMC_vs_DEMetro_Z 0.99 -2.592 0.0148 -0.473
Metro_vs_SMC 0.0 2.396 0.0233 0.437
Metro_vs_SMC 0.3 4.151 0.000265 0.758
Metro_vs_SMC 0.5 2.661 0.0126 0.486
Metro_vs_SMC 0.9 1.750 0.0907 0.319
Metro_vs_SMC 0.95 4.113 0.000294 0.751
Metro_vs_SMC 0.99 4.545 8.97e-05 0.830
Metro_vs_DEMetro_Z 0.0 -0.964 0.343 -0.176
Metro_vs_DEMetro_Z 0.3 0.650 0.521 0.119
Metro_vs_DEMetro_Z 0.5 -0.676 0.504 -0.123
Metro_vs_DEMetro_Z 0.9 1.396 0.173 0.255
Metro_vs_DEMetro_Z 0.95 3.184 0.00346 0.581
Metro_vs_DEMetro_Z 0.99 3.924 0.000492 0.716
HMC_vs_Metro 0.0 -1.799 0.0825 -0.328
HMC_vs_Metro 0.3 -2.642 0.0132 -0.482
HMC_vs_Metro 0.5 -1.325 0.195 -0.242
HMC_vs_Metro 0.9 -1.597 0.121 -0.292
HMC_vs_Metro 0.95 -3.421 0.00188 -0.625
HMC_vs_Metro 0.99 -4.347 0.000155 -0.794
HMC_vs_SMC 0.0 0.698 0.491 0.127
HMC_vs_SMC 0.3 2.762 0.00987 0.504
HMC_vs_SMC 0.5 2.241 0.0328 0.409
HMC_vs_SMC 0.9 2.554 0.0162 0.466
HMC_vs_SMC 0.95 3.437 0.0018 0.627
HMC_vs_SMC 0.99 2.060 0.0485 0.376
DEMetro_Z_vs_SMC 0.0 3.927 0.000488 0.717
DEMetro_Z_vs_SMC 0.3 4.214 0.000223 0.769
DEMetro_Z_vs_SMC 0.5 4.264 0.000195 0.779
DEMetro_Z_vs_SMC 0.9 3.149 0.00378 0.575
DEMetro_Z_vs_SMC 0.95 3.968 0.000436 0.724
DEMetro_Z_vs_SMC 0.99 3.453 0.00173 0.630
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.064 0.065 0.042 -0.012
HMC 0.3 0.084 0.056 0.040 0.709
HMC 0.5 0.092 0.068 0.046 0.513
HMC 0.9 0.090 0.047 0.027 1.631
HMC 0.95 0.112 0.053 0.037 1.591
HMC 0.99 0.099 0.061 0.047 0.815
SMC 0.0 0.057 0.065 0.042 -0.186
SMC 0.3 0.051 0.056 0.040 -0.130
SMC 0.5 0.070 0.068 0.046 0.040
SMC 0.9 0.056 0.047 0.027 0.324
SMC 0.95 0.057 0.053 0.037 0.114
SMC 0.99 0.059 0.061 0.047 -0.027
Metro 0.0 0.102 0.065 0.042 0.886
Metro 0.3 0.144 0.056 0.040 2.220
Metro 0.5 0.119 0.068 0.046 1.095
Metro 0.9 0.475 0.047 0.027 16.066
Metro 0.95 0.410 0.053 0.037 9.673
Metro 0.99 1.433 0.061 0.047 28.951
DEMetro_Z 0.0 0.129 0.065 0.042 1.537
DEMetro_Z 0.3 0.128 0.056 0.040 1.815
DEMetro_Z 0.5 0.134 0.068 0.046 1.426
DEMetro_Z 0.9 0.136 0.047 0.027 3.339
DEMetro_Z 0.95 0.133 0.053 0.037 2.175
DEMetro_Z 0.99 0.207 0.061 0.047 3.089
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -1.569 0.125 -0.309
HMC 0.3 1.396 0.171 0.672
HMC 0.5 1.072 0.293 1.596
HMC 0.9 0.151 0.881 0.043
HMC 0.95 0.314 0.755 0.123
HMC 0.99 -0.237 0.813 -0.053
SMC 0.0 -1.672 0.103 -0.331
SMC 0.3 0.541 0.59 0.148
SMC 0.5 0.370 0.713 0.094
SMC 0.9 -1.384 0.174 -0.285
SMC 0.95 -1.382 0.173 -0.308
SMC 0.99 -1.231 0.226 -0.241
Metro 0.0 -1.603 0.118 -0.308
Metro 0.3 1.097 0.278 0.381
Metro 0.5 0.396 0.694 0.098
Metro 0.9 0.995 0.327 1.248
Metro 0.95 0.795 0.432 0.504
Metro 0.99 2.425 0.0207 1.524
DEMetro_Z 0.0 -1.546 0.131 -0.297
DEMetro_Z 0.3 0.790 0.433 0.251
DEMetro_Z 0.5 0.537 0.594 0.135
DEMetro_Z 0.9 0.915 0.364 0.247
DEMetro_Z 0.95 -0.444 0.659 -0.100
DEMetro_Z 0.99 -0.564 0.576 -0.110
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 0.377 0.709 0.069
HMC_vs_SMC 0.3 1.212 0.235 0.221
HMC_vs_SMC 0.5 1.013 0.32 0.185
HMC_vs_SMC 0.9 1.438 0.161 0.263
HMC_vs_SMC 0.95 1.316 0.199 0.240
HMC_vs_SMC 0.99 1.501 0.144 0.274
Metro_vs_DEMetro_Z 0.0 -0.303 0.764 -0.055
Metro_vs_DEMetro_Z 0.3 0.761 0.453 0.139
Metro_vs_DEMetro_Z 0.5 -1.210 0.236 -0.221
Metro_vs_DEMetro_Z 0.9 0.788 0.437 0.144
Metro_vs_DEMetro_Z 0.95 1.025 0.314 0.187
Metro_vs_DEMetro_Z 0.99 2.720 0.0109 0.497
HMC_vs_Metro 0.0 -0.012 0.991 -0.002
HMC_vs_Metro 0.3 0.625 0.537 0.114
HMC_vs_Metro 0.5 1.020 0.316 0.186
HMC_vs_Metro 0.9 -0.947 0.352 -0.173
HMC_vs_Metro 0.95 -0.567 0.575 -0.103
HMC_vs_Metro 0.99 -2.516 0.0177 -0.459
HMC_vs_DEMetro_Z 0.0 -0.273 0.787 -0.050
HMC_vs_DEMetro_Z 0.3 1.024 0.314 0.187
HMC_vs_DEMetro_Z 0.5 0.986 0.332 0.180
HMC_vs_DEMetro_Z 0.9 -0.695 0.492 -0.127
HMC_vs_DEMetro_Z 0.95 0.751 0.458 0.137
HMC_vs_DEMetro_Z 0.99 0.526 0.603 0.096
Metro_vs_SMC 0.0 0.395 0.695 0.072
Metro_vs_SMC 0.3 1.206 0.238 0.220
Metro_vs_SMC 0.5 0.133 0.895 0.024
Metro_vs_SMC 0.9 1.239 0.225 0.226
Metro_vs_SMC 0.95 1.401 0.172 0.256
Metro_vs_SMC 0.99 2.913 0.00683 0.532
DEMetro_Z_vs_SMC 0.0 0.696 0.492 0.127
DEMetro_Z_vs_SMC 0.3 0.885 0.383 0.162
DEMetro_Z_vs_SMC 0.5 0.942 0.354 0.172
DEMetro_Z_vs_SMC 0.9 3.034 0.00506 0.554
DEMetro_Z_vs_SMC 0.95 3.681 0.000943 0.672
DEMetro_Z_vs_SMC 0.99 1.674 0.105 0.306
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 4.719 9.112 14.240 -0.309
HMC 0.3 8.039 4.697 4.977 0.672
HMC 0.5 47.348 9.883 23.480 1.596
HMC 0.9 5.657 5.328 7.624 0.043
HMC 0.95 7.739 6.496 10.111 0.123
HMC 0.99 4.903 5.445 10.256 -0.053
SMC 0.0 4.403 9.112 14.240 -0.331
SMC 0.3 5.435 4.697 4.977 0.148
SMC 0.5 12.079 9.883 23.480 0.094
SMC 0.9 3.155 5.328 7.624 -0.285
SMC 0.95 3.387 6.496 10.111 -0.308
SMC 0.99 2.973 5.445 10.256 -0.241
Metro 0.0 4.727 9.112 14.240 -0.308
Metro 0.3 6.593 4.697 4.977 0.381
Metro 0.5 12.180 9.883 23.480 0.098
Metro 0.9 14.847 5.328 7.624 1.248
Metro 0.95 11.597 6.496 10.111 0.504
Metro 0.99 21.071 5.445 10.256 1.524
DEMetro_Z 0.0 4.881 9.112 14.240 -0.297
DEMetro_Z 0.3 5.946 4.697 4.977 0.251
DEMetro_Z 0.5 13.057 9.883 23.480 0.135
DEMetro_Z 0.9 7.210 5.328 7.624 0.247
DEMetro_Z 0.95 5.489 6.496 10.111 -0.100
DEMetro_Z 0.99 4.318 5.445 10.256 -0.110
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 1.949 0.0574 0.719
HMC 0.3 3.948 0.000369 2.424
HMC 0.5 1.808 0.0807 3.048
HMC 0.9 5.039 7.42e-06 1.820
HMC 0.95 4.228 0.000191 4.039
HMC 0.99 5.311 6.26e-06 3.153
SMC 0.0 -0.278 0.782 -0.066
SMC 0.3 0.570 0.571 0.140
SMC 0.5 0.943 0.35 0.256
SMC 0.9 -0.490 0.626 -0.118
SMC 0.95 0.715 0.478 0.224
SMC 0.99 1.616 0.113 0.557
Metro 0.0 4.926 1.85e-05 2.680
Metro 0.3 6.119 6.38e-07 4.142
Metro 0.5 7.400 3.78e-09 3.060
Metro 0.9 2.300 0.0288 14.581
Metro 0.95 5.805 2.64e-06 15.821
Metro 0.99 5.682 3.81e-06 41.783
DEMetro_Z 0.0 8.153 6.49e-10 3.917
DEMetro_Z 0.3 8.543 5.35e-10 5.423
DEMetro_Z 0.5 8.995 5.35e-11 4.335
DEMetro_Z 0.9 4.955 2.54e-05 5.691
DEMetro_Z 0.95 9.087 2.23e-10 7.465
DEMetro_Z 0.99 6.116 8.26e-07 5.469
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 -1.657 0.108 -0.302
Metro_vs_DEMetro_Z 0.3 -1.478 0.15 -0.270
Metro_vs_DEMetro_Z 0.5 -2.637 0.0133 -0.481
Metro_vs_DEMetro_Z 0.9 1.350 0.187 0.247
Metro_vs_DEMetro_Z 0.95 2.943 0.00634 0.537
Metro_vs_DEMetro_Z 0.99 4.802 4.39e-05 0.877
DEMetro_Z_vs_SMC 0.0 8.149 5.5e-09 1.488
DEMetro_Z_vs_SMC 0.3 9.011 6.63e-10 1.645
DEMetro_Z_vs_SMC 0.5 9.290 3.41e-10 1.696
DEMetro_Z_vs_SMC 0.9 5.152 1.66e-05 0.941
DEMetro_Z_vs_SMC 0.95 9.055 5.97e-10 1.653
DEMetro_Z_vs_SMC 0.99 5.166 1.6e-05 0.943
HMC_vs_DEMetro_Z 0.0 -5.863 2.32e-06 -1.070
HMC_vs_DEMetro_Z 0.3 -3.495 0.00155 -0.638
HMC_vs_DEMetro_Z 0.5 -0.720 0.477 -0.131
HMC_vs_DEMetro_Z 0.9 -3.435 0.00181 -0.627
HMC_vs_DEMetro_Z 0.95 -4.524 9.51e-05 -0.826
HMC_vs_DEMetro_Z 0.99 -2.129 0.0419 -0.389
HMC_vs_Metro 0.0 -3.468 0.00166 -0.633
HMC_vs_Metro 0.3 -2.150 0.0401 -0.392
HMC_vs_Metro 0.5 -0.008 0.994 -0.001
HMC_vs_Metro 0.9 -2.014 0.0534 -0.368
HMC_vs_Metro 0.95 -3.986 0.000415 -0.728
HMC_vs_Metro 0.99 -5.236 1.32e-05 -0.956
HMC_vs_SMC 0.0 2.384 0.0239 0.435
HMC_vs_SMC 0.3 3.525 0.00143 0.643
HMC_vs_SMC 0.5 1.660 0.108 0.303
HMC_vs_SMC 0.9 6.305 6.93e-07 1.151
HMC_vs_SMC 0.95 4.030 0.000368 0.736
HMC_vs_SMC 0.99 3.834 0.000627 0.700
Metro_vs_SMC 0.0 5.373 9.01e-06 0.981
Metro_vs_SMC 0.3 6.450 4.67e-07 1.178
Metro_vs_SMC 0.5 8.808 1.08e-09 1.608
Metro_vs_SMC 0.9 2.313 0.028 0.422
Metro_vs_SMC 0.95 5.746 3.2e-06 1.049
Metro_vs_SMC 0.99 5.609 4.68e-06 1.024
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.149 0.124 0.035 0.719
HMC 0.3 0.182 0.116 0.027 2.424
HMC 0.5 0.230 0.120 0.036 3.048
HMC 0.9 0.176 0.115 0.034 1.820
HMC 0.95 0.210 0.111 0.025 4.039
HMC 0.99 0.236 0.111 0.040 3.153
SMC 0.0 0.122 0.124 0.035 -0.066
SMC 0.3 0.120 0.116 0.027 0.140
SMC 0.5 0.129 0.120 0.036 0.256
SMC 0.9 0.111 0.115 0.034 -0.118
SMC 0.95 0.116 0.111 0.025 0.224
SMC 0.99 0.133 0.111 0.040 0.557
Metro 0.0 0.217 0.124 0.035 2.680
Metro 0.3 0.229 0.116 0.027 4.142
Metro 0.5 0.231 0.120 0.036 3.060
Metro 0.9 0.605 0.115 0.034 14.581
Metro 0.95 0.499 0.111 0.025 15.821
Metro 0.99 1.763 0.111 0.040 41.783
DEMetro_Z 0.0 0.261 0.124 0.035 3.917
DEMetro_Z 0.3 0.263 0.116 0.027 5.423
DEMetro_Z 0.5 0.277 0.120 0.036 4.335
DEMetro_Z 0.9 0.306 0.115 0.034 5.691
DEMetro_Z 0.95 0.294 0.111 0.025 7.465
DEMetro_Z 0.99 0.327 0.111 0.040 5.469
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 2.850 0.00609 0.687
HMC 0.3 2.509 0.0175 2.346
HMC 0.5 3.705 0.000533 1.250
HMC 0.9 6.222 1.04e-07 2.111
HMC 0.95 5.630 2e-06 2.936
HMC 0.99 6.065 2.67e-07 2.359
SMC 0.0 1.382 0.173 0.462
SMC 0.3 2.033 0.0473 0.656
SMC 0.5 0.886 0.379 0.271
SMC 0.9 1.768 0.0825 0.506
SMC 0.95 5.059 8.06e-06 1.998
SMC 0.99 3.984 0.000257 1.600
Metro 0.0 8.124 8.92e-10 4.144
Metro 0.3 7.986 1.57e-09 4.269
Metro 0.5 7.556 1.02e-08 5.231
Metro 0.9 8.272 3.21e-09 12.398
Metro 0.95 9.779 8.96e-11 18.260
Metro 0.99 13.732 2.66e-14 34.098
DEMetro_Z 0.0 8.360 1.17e-09 5.987
DEMetro_Z 0.3 7.438 1.98e-08 6.552
DEMetro_Z 0.5 10.003 1.42e-11 6.876
DEMetro_Z 0.9 5.997 1.31e-06 6.756
DEMetro_Z 0.95 9.107 3.21e-10 10.135
DEMetro_Z 0.99 7.979 4.27e-09 6.687
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 7.036 9.74e-08 1.285
DEMetro_Z_vs_SMC 0.3 6.688 2.46e-07 1.221
DEMetro_Z_vs_SMC 0.5 9.400 2.64e-10 1.716
DEMetro_Z_vs_SMC 0.9 6.002 1.58e-06 1.096
DEMetro_Z_vs_SMC 0.95 7.330 4.48e-08 1.338
DEMetro_Z_vs_SMC 0.99 5.886 2.18e-06 1.075
HMC_vs_Metro 0.0 -7.322 4.59e-08 -1.337
HMC_vs_Metro 0.3 -2.289 0.0296 -0.418
HMC_vs_Metro 0.5 -5.749 3.18e-06 -1.050
HMC_vs_Metro 0.9 -6.643 2.77e-07 -1.213
HMC_vs_Metro 0.95 -8.552 2.02e-09 -1.561
HMC_vs_Metro 0.99 -12.600 2.74e-13 -2.300
Metro_vs_DEMetro_Z 0.0 -2.192 0.0365 -0.400
Metro_vs_DEMetro_Z 0.3 -2.128 0.042 -0.388
Metro_vs_DEMetro_Z 0.5 -1.700 0.0998 -0.310
Metro_vs_DEMetro_Z 0.9 2.812 0.00874 0.513
Metro_vs_DEMetro_Z 0.95 4.091 0.000312 0.747
Metro_vs_DEMetro_Z 0.99 9.650 1.47e-10 1.762
HMC_vs_SMC 0.0 0.765 0.45 0.140
HMC_vs_SMC 0.3 1.780 0.0856 0.325
HMC_vs_SMC 0.5 2.601 0.0145 0.475
HMC_vs_SMC 0.9 3.991 0.00041 0.729
HMC_vs_SMC 0.95 1.443 0.16 0.263
HMC_vs_SMC 0.99 1.343 0.19 0.245
Metro_vs_SMC 0.0 8.791 1.13e-09 1.605
Metro_vs_SMC 0.3 6.833 1.67e-07 1.247
Metro_vs_SMC 0.5 7.919 9.84e-09 1.446
Metro_vs_SMC 0.9 7.826 1.25e-08 1.429
Metro_vs_SMC 0.95 8.422 2.78e-09 1.538
Metro_vs_SMC 0.99 12.820 1.79e-13 2.341
HMC_vs_DEMetro_Z 0.0 -6.988 1.11e-07 -1.276
HMC_vs_DEMetro_Z 0.3 -3.231 0.00307 -0.590
HMC_vs_DEMetro_Z 0.5 -8.158 5.38e-09 -1.489
HMC_vs_DEMetro_Z 0.9 -4.213 0.000224 -0.769
HMC_vs_DEMetro_Z 0.95 -6.518 3.89e-07 -1.190
HMC_vs_DEMetro_Z 0.99 -4.357 0.000151 -0.796
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.018 0.015 0.005 0.687
HMC 0.3 0.024 0.015 0.004 2.346
HMC 0.5 0.020 0.015 0.004 1.250
HMC 0.9 0.024 0.014 0.005 2.111
HMC 0.95 0.025 0.014 0.004 2.936
HMC 0.99 0.032 0.015 0.007 2.359
SMC 0.0 0.017 0.015 0.005 0.462
SMC 0.3 0.017 0.015 0.004 0.656
SMC 0.5 0.016 0.015 0.004 0.271
SMC 0.9 0.017 0.014 0.005 0.506
SMC 0.95 0.021 0.014 0.004 1.998
SMC 0.99 0.027 0.015 0.007 1.600
Metro 0.0 0.034 0.015 0.005 4.144
Metro 0.3 0.032 0.015 0.004 4.269
Metro 0.5 0.036 0.015 0.004 5.231
Metro 0.9 0.073 0.014 0.005 12.398
Metro 0.95 0.081 0.014 0.004 18.260
Metro 0.99 0.257 0.015 0.007 34.098
DEMetro_Z 0.0 0.042 0.015 0.005 5.987
DEMetro_Z 0.3 0.042 0.015 0.004 6.552
DEMetro_Z 0.5 0.042 0.015 0.004 6.876
DEMetro_Z 0.9 0.046 0.014 0.005 6.756
DEMetro_Z 0.95 0.051 0.014 0.004 10.135
DEMetro_Z 0.99 0.063 0.015 0.007 6.687
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 0.144 0.886 0.037
HMC 0.3 1.196 0.237 0.329
HMC 0.5 0.990 0.326 0.289
HMC 0.9 3.385 0.00159 1.482
HMC 0.95 2.186 0.0338 0.782
HMC 0.99 2.149 0.0381 1.045
SMC 0.0 -1.278 0.207 -0.286
SMC 0.3 0.502 0.617 0.134
SMC 0.5 0.641 0.524 0.174
SMC 0.9 1.143 0.26 0.513
SMC 0.95 -0.089 0.929 -0.025
SMC 0.99 -0.639 0.525 -0.191
Metro 0.0 3.730 0.000532 1.409
Metro 0.3 3.103 0.00308 0.973
Metro 0.5 3.839 0.000481 2.120
Metro 0.9 3.749 0.000768 6.406
Metro 0.95 6.325 4.37e-07 5.376
Metro 0.99 3.898 0.000527 29.490
DEMetro_Z 0.0 3.631 0.000999 3.440
DEMetro_Z 0.3 3.474 0.00116 1.342
DEMetro_Z 0.5 3.883 0.00043 2.219
DEMetro_Z 0.9 4.712 4.21e-05 3.261
DEMetro_Z 0.95 4.222 0.000151 2.189
DEMetro_Z 0.99 3.620 0.000842 1.718
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 -3.489 0.00157 -0.637
HMC_vs_DEMetro_Z 0.3 -2.487 0.0189 -0.454
HMC_vs_DEMetro_Z 0.5 -3.101 0.00427 -0.566
HMC_vs_DEMetro_Z 0.9 -2.026 0.052 -0.370
HMC_vs_DEMetro_Z 0.95 -2.873 0.00753 -0.525
HMC_vs_DEMetro_Z 0.99 -0.984 0.333 -0.180
Metro_vs_SMC 0.0 4.773 4.77e-05 0.871
Metro_vs_SMC 0.3 2.842 0.00813 0.519
Metro_vs_SMC 0.5 4.000 0.000401 0.730
Metro_vs_SMC 0.9 3.251 0.00291 0.594
Metro_vs_SMC 0.95 6.506 4.02e-07 1.188
Metro_vs_SMC 0.99 3.905 0.000518 0.713
Metro_vs_DEMetro_Z 0.0 -2.011 0.0537 -0.367
Metro_vs_DEMetro_Z 0.3 -0.970 0.34 -0.177
Metro_vs_DEMetro_Z 0.5 -0.121 0.905 -0.022
Metro_vs_DEMetro_Z 0.9 1.662 0.107 0.303
Metro_vs_DEMetro_Z 0.95 3.265 0.00281 0.596
Metro_vs_DEMetro_Z 0.99 3.616 0.00112 0.660
HMC_vs_Metro 0.0 -3.909 0.000513 -0.714
HMC_vs_Metro 0.3 -3.161 0.00367 -0.577
HMC_vs_Metro 0.5 -3.332 0.00236 -0.608
HMC_vs_Metro 0.9 -2.964 0.00601 -0.541
HMC_vs_Metro 0.95 -5.227 1.35e-05 -0.954
HMC_vs_Metro 0.99 -3.732 0.000823 -0.681
HMC_vs_SMC 0.0 1.936 0.0626 0.354
HMC_vs_SMC 0.3 0.883 0.385 0.161
HMC_vs_SMC 0.5 0.507 0.616 0.092
HMC_vs_SMC 0.9 1.764 0.0882 0.322
HMC_vs_SMC 0.95 2.347 0.0259 0.429
HMC_vs_SMC 0.99 2.362 0.0251 0.431
DEMetro_Z_vs_SMC 0.0 3.811 0.000667 0.696
DEMetro_Z_vs_SMC 0.3 3.130 0.00396 0.571
DEMetro_Z_vs_SMC 0.5 3.421 0.00187 0.625
DEMetro_Z_vs_SMC 0.9 3.564 0.00129 0.651
DEMetro_Z_vs_SMC 0.95 3.976 0.000427 0.726
DEMetro_Z_vs_SMC 0.99 4.494 0.000103 0.820
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.066 0.065 0.042 0.037
HMC 0.3 0.069 0.056 0.040 0.329
HMC 0.5 0.082 0.068 0.046 0.289
HMC 0.9 0.086 0.047 0.027 1.482
HMC 0.95 0.082 0.053 0.037 0.782
HMC 0.99 0.110 0.061 0.047 1.045
SMC 0.0 0.053 0.065 0.042 -0.286
SMC 0.3 0.061 0.056 0.040 0.134
SMC 0.5 0.076 0.068 0.046 0.174
SMC 0.9 0.061 0.047 0.027 0.513
SMC 0.95 0.052 0.053 0.037 -0.025
SMC 0.99 0.052 0.061 0.047 -0.191
Metro 0.0 0.124 0.065 0.042 1.409
Metro 0.3 0.094 0.056 0.040 0.973
Metro 0.5 0.167 0.068 0.046 2.120
Metro 0.9 0.218 0.047 0.027 6.406
Metro 0.95 0.251 0.053 0.037 5.376
Metro 0.99 1.458 0.061 0.047 29.490
DEMetro_Z 0.0 0.209 0.065 0.042 3.440
DEMetro_Z 0.3 0.109 0.056 0.040 1.342
DEMetro_Z 0.5 0.171 0.068 0.046 2.219
DEMetro_Z 0.9 0.134 0.047 0.027 3.261
DEMetro_Z 0.95 0.134 0.053 0.037 2.189
DEMetro_Z 0.99 0.142 0.061 0.047 1.718
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -0.900 0.372 -0.213
HMC 0.3 1.080 0.289 1.582
HMC 0.5 0.344 0.732 0.087
HMC 0.9 -0.338 0.737 -0.078
HMC 0.95 0.588 0.559 0.163
HMC 0.99 0.240 0.811 0.073
SMC 0.0 -2.116 0.0418 -0.402
SMC 0.3 1.040 0.307 3.162
SMC 0.5 0.471 0.639 0.119
SMC 0.9 -0.296 0.768 -0.072
SMC 0.95 -1.327 0.191 -0.288
SMC 0.99 -1.609 0.117 -0.308
Metro 0.0 -1.167 0.249 -0.249
Metro 0.3 0.535 0.595 0.169
Metro 0.5 0.673 0.504 0.174
Metro 0.9 0.119 0.906 0.027
Metro 0.95 -0.372 0.711 -0.083
Metro 0.99 1.284 0.209 1.285
DEMetro_Z 0.0 0.431 0.669 0.182
DEMetro_Z 0.3 0.900 0.373 0.286
DEMetro_Z 0.5 0.499 0.62 0.126
DEMetro_Z 0.9 -0.434 0.666 -0.096
DEMetro_Z 0.95 -0.169 0.866 -0.041
DEMetro_Z 0.99 -0.825 0.415 -0.159
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 1.281 0.21 0.234
HMC_vs_SMC 0.3 -0.469 0.642 -0.086
HMC_vs_SMC 0.5 -0.522 0.606 -0.095
HMC_vs_SMC 0.9 -0.039 0.969 -0.007
HMC_vs_SMC 0.95 2.428 0.0216 0.443
HMC_vs_SMC 0.99 1.571 0.127 0.287
Metro_vs_DEMetro_Z 0.0 -1.072 0.293 -0.196
Metro_vs_DEMetro_Z 0.3 -1.906 0.0666 -0.348
Metro_vs_DEMetro_Z 0.5 0.651 0.52 0.119
Metro_vs_DEMetro_Z 0.9 1.219 0.233 0.223
Metro_vs_DEMetro_Z 0.95 -0.429 0.671 -0.078
Metro_vs_DEMetro_Z 0.99 1.531 0.137 0.280
HMC_vs_Metro 0.0 0.200 0.843 0.037
HMC_vs_Metro 0.3 0.972 0.339 0.177
HMC_vs_Metro 0.5 -1.229 0.229 -0.224
HMC_vs_Metro 0.9 -0.816 0.421 -0.149
HMC_vs_Metro 0.95 1.244 0.223 0.227
HMC_vs_Metro 0.99 -1.224 0.231 -0.223
HMC_vs_DEMetro_Z 0.0 -0.944 0.353 -0.172
HMC_vs_DEMetro_Z 0.3 0.880 0.386 0.161
HMC_vs_DEMetro_Z 0.5 -1.349 0.188 -0.246
HMC_vs_DEMetro_Z 0.9 0.203 0.841 0.037
HMC_vs_DEMetro_Z 0.95 0.985 0.333 0.180
HMC_vs_DEMetro_Z 0.99 0.929 0.36 0.170
Metro_vs_SMC 0.0 1.465 0.154 0.268
Metro_vs_SMC 0.3 -1.001 0.325 -0.183
Metro_vs_SMC 0.5 0.611 0.546 0.112
Metro_vs_SMC 0.9 0.643 0.526 0.117
Metro_vs_SMC 0.95 5.610 4.67e-06 1.024
Metro_vs_SMC 0.99 1.681 0.104 0.307
DEMetro_Z_vs_SMC 0.0 1.501 0.144 0.274
DEMetro_Z_vs_SMC 0.3 -0.965 0.343 -0.176
DEMetro_Z_vs_SMC 0.5 0.104 0.918 0.019
DEMetro_Z_vs_SMC 0.9 -0.180 0.859 -0.033
DEMetro_Z_vs_SMC 0.95 2.664 0.0125 0.486
DEMetro_Z_vs_SMC 0.99 2.964 0.00601 0.541
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 6.074 9.112 14.240 -0.213
HMC 0.3 12.569 4.697 4.977 1.582
HMC 0.5 11.918 9.883 23.480 0.087
HMC 0.9 4.735 5.328 7.624 -0.078
HMC 0.95 8.144 6.496 10.111 0.163
HMC 0.99 6.197 5.445 10.256 0.073
SMC 0.0 3.390 9.112 14.240 -0.402
SMC 0.3 20.434 4.697 4.977 3.162
SMC 0.5 12.681 9.883 23.480 0.119
SMC 0.9 4.781 5.328 7.624 -0.072
SMC 0.95 3.584 6.496 10.111 -0.288
SMC 0.99 2.286 5.445 10.256 -0.308
Metro 0.0 5.560 9.112 14.240 -0.249
Metro 0.3 5.537 4.697 4.977 0.169
Metro 0.5 13.964 9.883 23.480 0.174
Metro 0.9 5.534 5.328 7.624 0.027
Metro 0.95 5.660 6.496 10.111 -0.083
Metro 0.99 18.624 5.445 10.256 1.285
DEMetro_Z 0.0 11.710 9.112 14.240 0.182
DEMetro_Z 0.3 6.119 4.697 4.977 0.286
DEMetro_Z 0.5 12.836 9.883 23.480 0.126
DEMetro_Z 0.9 4.597 5.328 7.624 -0.096
DEMetro_Z 0.95 6.079 6.496 10.111 -0.041
DEMetro_Z 0.99 3.810 5.445 10.256 -0.159
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 2.659 0.0105 0.885
HMC 0.3 1.647 0.11 2.041
HMC 0.5 3.316 0.00194 1.467
HMC 0.9 5.138 4.49e-06 1.687
HMC 0.95 4.939 2.4e-05 4.146
HMC 0.99 4.228 0.000155 2.347
SMC 0.0 -1.215 0.23 -0.271
SMC 0.3 1.149 0.258 0.548
SMC 0.5 2.071 0.0428 0.540
SMC 0.9 0.493 0.624 0.156
SMC 0.95 0.056 0.956 0.018
SMC 0.99 0.695 0.49 0.228
Metro 0.0 3.937 0.000424 3.447
Metro 0.3 7.021 1.09e-08 2.759
Metro 0.5 5.508 4.4e-06 4.334
Metro 0.9 6.616 2.11e-07 6.411
Metro 0.95 12.351 1.6e-13 12.155
Metro 0.99 5.137 1.73e-05 40.023
DEMetro_Z 0.0 4.177 0.000235 6.062
DEMetro_Z 0.3 8.724 1.28e-10 4.276
DEMetro_Z 0.5 8.201 8.55e-10 4.412
DEMetro_Z 0.9 9.383 1.31e-11 4.300
DEMetro_Z 0.95 4.216 0.000215 7.501
DEMetro_Z 0.99 8.148 6.64e-10 3.922
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 -1.519 0.14 -0.277
Metro_vs_DEMetro_Z 0.3 -3.185 0.00345 -0.581
Metro_vs_DEMetro_Z 0.5 -0.080 0.937 -0.015
Metro_vs_DEMetro_Z 0.9 2.216 0.0347 0.404
Metro_vs_DEMetro_Z 0.95 2.124 0.0423 0.388
Metro_vs_DEMetro_Z 0.99 4.614 7.4e-05 0.842
DEMetro_Z_vs_SMC 0.0 4.292 0.00018 0.784
DEMetro_Z_vs_SMC 0.3 6.249 8.06e-07 1.141
DEMetro_Z_vs_SMC 0.5 7.005 1.06e-07 1.279
DEMetro_Z_vs_SMC 0.9 8.594 1.82e-09 1.569
DEMetro_Z_vs_SMC 0.95 4.147 0.000268 0.757
DEMetro_Z_vs_SMC 0.99 7.570 2.41e-08 1.382
HMC_vs_DEMetro_Z 0.0 -3.398 0.00199 -0.620
HMC_vs_DEMetro_Z 0.3 -1.613 0.118 -0.294
HMC_vs_DEMetro_Z 0.5 -4.845 3.91e-05 -0.884
HMC_vs_DEMetro_Z 0.9 -4.551 8.82e-05 -0.831
HMC_vs_DEMetro_Z 0.95 -1.715 0.0969 -0.313
HMC_vs_DEMetro_Z 0.99 -2.091 0.0454 -0.382
HMC_vs_Metro 0.0 -2.819 0.00859 -0.515
HMC_vs_Metro 0.3 -0.641 0.526 -0.117
HMC_vs_Metro 0.5 -3.308 0.00252 -0.604
HMC_vs_Metro 0.9 -4.832 4.05e-05 -0.882
HMC_vs_Metro 0.95 -5.857 2.36e-06 -1.069
HMC_vs_Metro 0.99 -4.830 4.07e-05 -0.882
HMC_vs_SMC 0.0 4.600 7.69e-05 0.840
HMC_vs_SMC 0.3 1.152 0.259 0.210
HMC_vs_SMC 0.5 2.270 0.0308 0.414
HMC_vs_SMC 0.9 4.069 0.000332 0.743
HMC_vs_SMC 0.95 4.669 6.36e-05 0.852
HMC_vs_SMC 0.99 3.654 0.00101 0.667
Metro_vs_SMC 0.0 4.327 0.000164 0.790
Metro_vs_SMC 0.3 3.995 0.000406 0.729
Metro_vs_SMC 0.5 5.046 2.23e-05 0.921
Metro_vs_SMC 0.9 6.186 9.57e-07 1.129
Metro_vs_SMC 0.95 12.614 2.67e-13 2.303
Metro_vs_SMC 0.99 5.075 2.06e-05 0.926
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.155 0.124 0.035 0.885
HMC 0.3 0.172 0.116 0.027 2.041
HMC 0.5 0.173 0.120 0.036 1.467
HMC 0.9 0.171 0.115 0.034 1.687
HMC 0.95 0.212 0.111 0.025 4.146
HMC 0.99 0.204 0.111 0.040 2.347
SMC 0.0 0.114 0.124 0.035 -0.271
SMC 0.3 0.131 0.116 0.027 0.548
SMC 0.5 0.139 0.120 0.036 0.540
SMC 0.9 0.120 0.115 0.034 0.156
SMC 0.95 0.111 0.111 0.025 0.018
SMC 0.99 0.120 0.111 0.040 0.228
Metro 0.0 0.244 0.124 0.035 3.447
Metro 0.3 0.191 0.116 0.027 2.759
Metro 0.5 0.277 0.120 0.036 4.334
Metro 0.9 0.330 0.115 0.034 6.411
Metro 0.95 0.409 0.111 0.025 12.155
Metro 0.99 1.694 0.111 0.040 40.023
DEMetro_Z 0.0 0.336 0.124 0.035 6.062
DEMetro_Z 0.3 0.232 0.116 0.027 4.276
DEMetro_Z 0.5 0.280 0.120 0.036 4.412
DEMetro_Z 0.9 0.259 0.115 0.034 4.300
DEMetro_Z 0.95 0.295 0.111 0.025 7.501
DEMetro_Z 0.99 0.266 0.111 0.040 3.922
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 3.640 0.000643 1.201
HMC 0.3 2.862 0.00612 0.941
HMC 0.5 2.668 0.0116 1.724
HMC 0.9 4.027 0.00026 1.976
HMC 0.95 5.801 1.41e-06 3.442
HMC 0.99 5.854 3.99e-07 2.013
SMC 0.0 0.564 0.575 0.153
SMC 0.3 1.750 0.0876 0.766
SMC 0.5 1.862 0.0686 0.632
SMC 0.9 1.892 0.0641 0.605
SMC 0.95 1.928 0.06 0.706
SMC 0.99 2.867 0.0063 1.095
Metro 0.0 9.213 2.76e-11 4.420
Metro 0.3 7.464 5.44e-09 3.598
Metro 0.5 8.291 1.6e-09 6.358
Metro 0.9 13.684 1.12e-15 7.943
Metro 0.95 12.289 3.39e-13 19.185
Metro 0.99 10.301 3.19e-11 40.306
DEMetro_Z 0.0 7.584 1.09e-08 5.721
DEMetro_Z 0.3 8.617 2.47e-10 4.588
DEMetro_Z 0.5 9.691 1.86e-11 5.706
DEMetro_Z 0.9 10.172 2.01e-12 4.967
DEMetro_Z 0.95 7.462 2.06e-08 7.323
DEMetro_Z 0.99 7.979 6.95e-10 3.437
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 7.540 2.6e-08 1.377
DEMetro_Z_vs_SMC 0.3 5.198 1.46e-05 0.949
DEMetro_Z_vs_SMC 0.5 7.453 3.26e-08 1.361
DEMetro_Z_vs_SMC 0.9 7.930 9.57e-09 1.448
DEMetro_Z_vs_SMC 0.95 6.477 4.34e-07 1.183
DEMetro_Z_vs_SMC 0.99 4.326 0.000164 0.790
HMC_vs_Metro 0.0 -5.558 5.39e-06 -1.015
HMC_vs_Metro 0.3 -5.310 1.07e-05 -0.970
HMC_vs_Metro 0.5 -4.387 0.000139 -0.801
HMC_vs_Metro 0.9 -7.959 8.89e-09 -1.453
HMC_vs_Metro 0.95 -9.189 4.34e-10 -1.678
HMC_vs_Metro 0.99 -9.856 9.16e-11 -1.799
Metro_vs_DEMetro_Z 0.0 -1.705 0.099 -0.311
Metro_vs_DEMetro_Z 0.3 -1.659 0.108 -0.303
Metro_vs_DEMetro_Z 0.5 0.669 0.509 0.122
Metro_vs_DEMetro_Z 0.9 3.979 0.000424 0.726
Metro_vs_DEMetro_Z 0.95 6.561 3.46e-07 1.198
Metro_vs_DEMetro_Z 0.99 9.283 3.47e-10 1.695
HMC_vs_SMC 0.0 4.541 9.06e-05 0.829
HMC_vs_SMC 0.3 0.418 0.679 0.076
HMC_vs_SMC 0.5 1.662 0.107 0.303
HMC_vs_SMC 0.9 2.607 0.0143 0.476
HMC_vs_SMC 0.95 4.387 0.000139 0.801
HMC_vs_SMC 0.99 1.806 0.0813 0.330
Metro_vs_SMC 0.0 8.331 3.49e-09 1.521
Metro_vs_SMC 0.3 4.333 0.000161 0.791
Metro_vs_SMC 0.5 7.318 4.63e-08 1.336
Metro_vs_SMC 0.9 10.677 1.46e-11 1.949
Metro_vs_SMC 0.95 12.304 4.92e-13 2.246
Metro_vs_SMC 0.99 9.857 9.15e-11 1.800
HMC_vs_DEMetro_Z 0.0 -5.545 5.58e-06 -1.012
HMC_vs_DEMetro_Z 0.3 -6.256 7.9e-07 -1.142
HMC_vs_DEMetro_Z 0.5 -5.287 1.14e-05 -0.965
HMC_vs_DEMetro_Z 0.9 -4.060 0.000339 -0.741
HMC_vs_DEMetro_Z 0.95 -3.625 0.00109 -0.662
HMC_vs_DEMetro_Z 0.99 -2.807 0.00884 -0.513
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.020 0.015 0.005 1.201
HMC 0.3 0.019 0.015 0.004 0.941
HMC 0.5 0.022 0.015 0.004 1.724
HMC 0.9 0.024 0.014 0.005 1.976
HMC 0.95 0.027 0.014 0.004 3.442
HMC 0.99 0.030 0.015 0.007 2.013
SMC 0.0 0.015 0.015 0.005 0.153
SMC 0.3 0.018 0.015 0.004 0.766
SMC 0.5 0.017 0.015 0.004 0.632
SMC 0.9 0.017 0.014 0.005 0.605
SMC 0.95 0.017 0.014 0.004 0.706
SMC 0.99 0.023 0.015 0.007 1.095
Metro 0.0 0.035 0.015 0.005 4.420
Metro 0.3 0.029 0.015 0.004 3.598
Metro 0.5 0.040 0.015 0.004 6.358
Metro 0.9 0.052 0.014 0.005 7.943
Metro 0.95 0.084 0.014 0.004 19.185
Metro 0.99 0.301 0.015 0.007 40.306
DEMetro_Z 0.0 0.041 0.015 0.005 5.721
DEMetro_Z 0.3 0.034 0.015 0.004 4.588
DEMetro_Z 0.5 0.038 0.015 0.004 5.706
DEMetro_Z 0.9 0.038 0.014 0.005 4.967
DEMetro_Z 0.95 0.041 0.014 0.004 7.323
DEMetro_Z 0.99 0.040 0.015 0.007 3.437
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Forest & Ridge Plots
Pooled
0.0 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.9 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.95 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.99 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
0.0 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.9 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.95 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.99 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
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0.3
0.5
0.9
0.95
0.99
Chain
0.0
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Vary_Correlation_with_high_Multimodality (Mixture, correlation, 30 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 7.138 7.28e-08 31.388
HMC 0.3 7.170 6.64e-08 26.126
HMC 0.5 7.110 7.75e-08 25.148
HMC 0.9 7.465 2.92e-08 17.001
HMC 0.95 8.276 3.71e-09 21.745
HMC 0.99 6.668 2.24e-07 10.076
SMC 0.0 1.246 0.218 0.335
SMC 0.3 -0.539 0.592 -0.126
SMC 0.5 -1.234 0.223 -0.278
SMC 0.9 -0.683 0.498 -0.144
SMC 0.95 -0.845 0.402 -0.209
SMC 0.99 1.460 0.15 0.382
Metro 0.0 7.044 8.29e-08 11.557
Metro 0.3 6.363 5.17e-07 9.473
Metro 0.5 5.329 9.56e-06 9.559
Metro 0.9 5.229 1.13e-05 5.401
Metro 0.95 6.927 1.06e-07 9.165
Metro 0.99 6.103 1.07e-06 9.552
DEMetro_Z 0.0 6.243 7.68e-07 13.316
DEMetro_Z 0.3 6.306 6.57e-07 15.388
DEMetro_Z 0.5 6.337 5.88e-07 12.576
DEMetro_Z 0.9 6.605 2.82e-07 12.854
DEMetro_Z 0.95 6.023 1.31e-06 8.526
DEMetro_Z 0.99 6.209 6.12e-07 5.301
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 3.527 0.00142 0.644
HMC_vs_DEMetro_Z 0.3 2.410 0.0225 0.440
HMC_vs_DEMetro_Z 0.5 3.209 0.00324 0.586
HMC_vs_DEMetro_Z 0.9 1.387 0.176 0.253
HMC_vs_DEMetro_Z 0.95 3.957 0.00045 0.722
HMC_vs_DEMetro_Z 0.99 2.943 0.00634 0.537
Metro_vs_SMC 0.0 6.716 2.28e-07 1.226
Metro_vs_SMC 0.3 6.328 6.5e-07 1.155
Metro_vs_SMC 0.5 5.442 7.42e-06 0.994
Metro_vs_SMC 0.9 5.499 6.34e-06 1.004
Metro_vs_SMC 0.95 6.779 1.93e-07 1.238
Metro_vs_SMC 0.99 5.776 2.95e-06 1.054
Metro_vs_DEMetro_Z 0.0 -0.678 0.503 -0.124
Metro_vs_DEMetro_Z 0.3 -1.786 0.0846 -0.326
Metro_vs_DEMetro_Z 0.5 -1.186 0.245 -0.217
Metro_vs_DEMetro_Z 0.9 -3.585 0.00122 -0.655
Metro_vs_DEMetro_Z 0.95 0.313 0.757 0.057
Metro_vs_DEMetro_Z 0.99 2.895 0.00713 0.529
HMC_vs_Metro 0.0 4.070 0.00033 0.743
HMC_vs_Metro 0.3 4.460 0.000113 0.814
HMC_vs_Metro 0.5 4.038 0.000361 0.737
HMC_vs_Metro 0.9 4.784 4.62e-05 0.873
HMC_vs_Metro 0.95 4.695 5.92e-05 0.857
HMC_vs_Metro 0.99 0.227 0.822 0.041
HMC_vs_SMC 0.0 6.965 1.17e-07 1.272
HMC_vs_SMC 0.3 7.093 8.37e-08 1.295
HMC_vs_SMC 0.5 7.173 6.78e-08 1.310
HMC_vs_SMC 0.9 7.545 2.57e-08 1.377
HMC_vs_SMC 0.95 8.471 2.47e-09 1.547
HMC_vs_SMC 0.99 6.371 5.79e-07 1.163
DEMetro_Z_vs_SMC 0.0 6.112 1.17e-06 1.116
DEMetro_Z_vs_SMC 0.3 6.390 5.49e-07 1.167
DEMetro_Z_vs_SMC 0.5 6.413 5.17e-07 1.171
DEMetro_Z_vs_SMC 0.9 6.684 2.48e-07 1.220
DEMetro_Z_vs_SMC 0.95 6.071 1.31e-06 1.108
DEMetro_Z_vs_SMC 0.99 5.850 2.41e-06 1.068
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 1.110 0.052 0.034 31.388
HMC 0.3 1.005 0.054 0.036 26.126
HMC 0.5 0.942 0.051 0.035 25.148
HMC 0.9 0.409 0.030 0.022 17.001
HMC 0.95 0.352 0.023 0.015 21.745
HMC 0.99 0.133 0.018 0.011 10.076
SMC 0.0 0.063 0.052 0.034 0.335
SMC 0.3 0.049 0.054 0.036 -0.126
SMC 0.5 0.041 0.051 0.035 -0.278
SMC 0.9 0.027 0.030 0.022 -0.144
SMC 0.95 0.020 0.023 0.015 -0.209
SMC 0.99 0.022 0.018 0.011 0.382
Metro 0.0 0.441 0.052 0.034 11.557
Metro 0.3 0.399 0.054 0.036 9.473
Metro 0.5 0.390 0.051 0.035 9.559
Metro 0.9 0.150 0.030 0.022 5.401
Metro 0.95 0.162 0.023 0.015 9.165
Metro 0.99 0.127 0.018 0.011 9.552
DEMetro_Z 0.0 0.501 0.052 0.034 13.316
DEMetro_Z 0.3 0.614 0.054 0.036 15.388
DEMetro_Z 0.5 0.497 0.051 0.035 12.576
DEMetro_Z 0.9 0.316 0.030 0.022 12.854
DEMetro_Z 0.95 0.152 0.023 0.015 8.526
DEMetro_Z 0.99 0.079 0.018 0.011 5.301
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 4.402 0.000133 35.278
HMC 0.3 4.585 8e-05 31.432
HMC 0.5 4.159 0.000259 24.917
HMC 0.9 3.680 0.000938 10.492
HMC 0.95 4.161 0.000248 6.551
HMC 0.99 5.048 1.17e-05 2.542
SMC 0.0 -1.026 0.309 -0.245
SMC 0.3 1.087 0.282 0.301
SMC 0.5 -0.091 0.928 -0.023
SMC 0.9 1.646 0.105 0.464
SMC 0.95 -0.820 0.416 -0.180
SMC 0.99 0.397 0.693 0.105
Metro 0.0 4.690 5.24e-05 4.795
Metro 0.3 4.608 6.8e-05 5.314
Metro 0.5 3.793 0.000665 4.776
Metro 0.9 7.827 6.19e-09 6.361
Metro 0.95 6.414 2.13e-07 3.727
Metro 0.99 6.188 7.7e-07 7.108
DEMetro_Z 0.0 3.253 0.00286 6.842
DEMetro_Z 0.3 3.358 0.0022 12.056
DEMetro_Z 0.5 3.153 0.00371 7.114
DEMetro_Z 0.9 4.414 0.000125 8.497
DEMetro_Z 0.95 4.201 0.000168 2.344
DEMetro_Z 0.99 5.581 2.66e-06 3.210
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 4.426 0.000125 0.808
HMC_vs_SMC 0.3 4.513 9.8e-05 0.824
HMC_vs_SMC 0.5 4.160 0.000258 0.760
HMC_vs_SMC 0.9 3.472 0.00164 0.634
HMC_vs_SMC 0.95 4.270 0.000191 0.780
HMC_vs_SMC 0.99 4.917 3.2e-05 0.898
Metro_vs_DEMetro_Z 0.0 -0.895 0.378 -0.163
Metro_vs_DEMetro_Z 0.3 -1.680 0.104 -0.307
Metro_vs_DEMetro_Z 0.5 -0.989 0.331 -0.181
Metro_vs_DEMetro_Z 0.9 -1.022 0.315 -0.187
Metro_vs_DEMetro_Z 0.95 1.909 0.0662 0.349
Metro_vs_DEMetro_Z 0.99 3.859 0.000587 0.704
HMC_vs_Metro 0.0 3.676 0.000957 0.671
HMC_vs_Metro 0.3 3.799 0.000688 0.694
HMC_vs_Metro 0.5 3.231 0.00306 0.590
HMC_vs_Metro 0.9 1.380 0.178 0.252
HMC_vs_Metro 0.95 1.710 0.0979 0.312
HMC_vs_Metro 0.99 -3.804 0.000679 -0.695
HMC_vs_DEMetro_Z 0.0 3.356 0.00222 0.613
HMC_vs_DEMetro_Z 0.3 2.458 0.0202 0.449
HMC_vs_DEMetro_Z 0.5 2.761 0.0099 0.504
HMC_vs_DEMetro_Z 0.9 0.529 0.601 0.097
HMC_vs_DEMetro_Z 0.95 2.409 0.0226 0.440
HMC_vs_DEMetro_Z 0.99 -1.025 0.314 -0.187
Metro_vs_SMC 0.0 4.712 5.65e-05 0.860
Metro_vs_SMC 0.3 4.425 0.000125 0.808
Metro_vs_SMC 0.5 3.826 0.000641 0.698
Metro_vs_SMC 0.9 7.303 4.82e-08 1.333
Metro_vs_SMC 0.95 6.892 1.42e-07 1.258
Metro_vs_SMC 0.99 6.373 5.76e-07 1.164
DEMetro_Z_vs_SMC 0.0 3.446 0.00175 0.629
DEMetro_Z_vs_SMC 0.3 3.265 0.00281 0.596
DEMetro_Z_vs_SMC 0.5 3.173 0.00355 0.579
DEMetro_Z_vs_SMC 0.9 4.118 0.00029 0.752
DEMetro_Z_vs_SMC 0.95 4.605 7.59e-05 0.841
DEMetro_Z_vs_SMC 0.99 5.684 3.8e-06 1.038
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 2.677 0.108 0.073 35.278
HMC 0.3 2.134 0.096 0.065 31.432
HMC 0.5 1.946 0.100 0.074 24.917
HMC 0.9 0.331 0.049 0.027 10.492
HMC 0.95 0.247 0.047 0.030 6.551
HMC 0.99 0.071 0.028 0.017 2.542
SMC 0.0 0.091 0.108 0.073 -0.245
SMC 0.3 0.116 0.096 0.065 0.301
SMC 0.5 0.099 0.100 0.074 -0.023
SMC 0.9 0.061 0.049 0.027 0.464
SMC 0.95 0.042 0.047 0.030 -0.180
SMC 0.99 0.030 0.028 0.017 0.105
Metro 0.0 0.458 0.108 0.073 4.795
Metro 0.3 0.441 0.096 0.065 5.314
Metro 0.5 0.454 0.100 0.074 4.776
Metro 0.9 0.220 0.049 0.027 6.361
Metro 0.95 0.161 0.047 0.030 3.727
Metro 0.99 0.147 0.028 0.017 7.108
DEMetro_Z 0.0 0.607 0.108 0.073 6.842
DEMetro_Z 0.3 0.878 0.096 0.065 12.056
DEMetro_Z 0.5 0.627 0.100 0.074 7.114
DEMetro_Z 0.9 0.278 0.049 0.027 8.497
DEMetro_Z 0.95 0.119 0.047 0.030 2.344
DEMetro_Z 0.99 0.082 0.028 0.017 3.210
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 6.950 1.21e-07 37.188
HMC 0.3 7.031 9.68e-08 31.100
HMC 0.5 7.012 1.02e-07 30.947
HMC 0.9 7.356 3.96e-08 19.733
HMC 0.95 7.971 8.27e-09 26.975
HMC 0.99 7.139 6.6e-08 12.901
SMC 0.0 1.263 0.212 0.348
SMC 0.3 -0.556 0.581 -0.125
SMC 0.5 -1.379 0.174 -0.306
SMC 0.9 -0.907 0.369 -0.188
SMC 0.95 -0.187 0.852 -0.045
SMC 0.99 1.287 0.203 0.345
Metro 0.0 7.065 8.11e-08 13.329
Metro 0.3 6.541 3.26e-07 10.841
Metro 0.5 5.303 1.05e-05 11.675
Metro 0.9 6.420 3.93e-07 7.031
Metro 0.95 7.681 1.52e-08 12.258
Metro 0.99 8.039 6.34e-09 15.257
DEMetro_Z 0.0 6.336 6.06e-07 15.762
DEMetro_Z 0.3 6.410 5e-07 17.545
DEMetro_Z 0.5 6.337 6.04e-07 15.416
DEMetro_Z 0.9 6.978 1.04e-07 14.535
DEMetro_Z 0.95 6.220 8e-07 11.225
DEMetro_Z 0.99 7.782 9.31e-09 8.289
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 -0.808 0.426 -0.147
Metro_vs_DEMetro_Z 0.3 -1.806 0.0813 -0.330
Metro_vs_DEMetro_Z 0.5 -1.210 0.236 -0.221
Metro_vs_DEMetro_Z 0.9 -3.325 0.00241 -0.607
Metro_vs_DEMetro_Z 0.95 0.422 0.676 0.077
Metro_vs_DEMetro_Z 0.99 3.621 0.00111 0.661
DEMetro_Z_vs_SMC 0.0 6.274 7.53e-07 1.145
DEMetro_Z_vs_SMC 0.3 6.481 4.29e-07 1.183
DEMetro_Z_vs_SMC 0.5 6.425 4.99e-07 1.173
DEMetro_Z_vs_SMC 0.9 7.008 1.05e-07 1.279
DEMetro_Z_vs_SMC 0.95 6.204 9.13e-07 1.133
DEMetro_Z_vs_SMC 0.99 7.734 1.58e-08 1.412
HMC_vs_DEMetro_Z 0.0 3.475 0.00163 0.635
HMC_vs_DEMetro_Z 0.3 2.584 0.0151 0.472
HMC_vs_DEMetro_Z 0.5 3.138 0.00389 0.573
HMC_vs_DEMetro_Z 0.9 1.516 0.14 0.277
HMC_vs_DEMetro_Z 0.95 3.633 0.00107 0.663
HMC_vs_DEMetro_Z 0.99 2.308 0.0283 0.421
HMC_vs_Metro 0.0 4.071 0.00033 0.743
HMC_vs_Metro 0.3 4.503 0.000101 0.822
HMC_vs_Metro 0.5 4.072 0.000329 0.744
HMC_vs_Metro 0.9 4.493 0.000103 0.820
HMC_vs_Metro 0.95 4.263 0.000195 0.778
HMC_vs_Metro 0.99 -0.822 0.418 -0.150
HMC_vs_SMC 0.0 6.802 1.81e-07 1.242
HMC_vs_SMC 0.3 6.962 1.18e-07 1.271
HMC_vs_SMC 0.5 7.073 8.82e-08 1.291
HMC_vs_SMC 0.9 7.429 3.47e-08 1.356
HMC_vs_SMC 0.95 8.031 7.41e-09 1.466
HMC_vs_SMC 0.99 6.956 1.2e-07 1.270
Metro_vs_SMC 0.0 6.764 2.01e-07 1.235
Metro_vs_SMC 0.3 6.524 3.82e-07 1.191
Metro_vs_SMC 0.5 5.392 8.54e-06 0.984
Metro_vs_SMC 0.9 6.758 2.04e-07 1.234
Metro_vs_SMC 0.95 7.430 3.46e-08 1.357
Metro_vs_SMC 0.99 7.763 1.46e-08 1.417
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 1.023 0.063 0.026 37.188
HMC 0.3 0.935 0.064 0.028 31.100
HMC 0.5 0.860 0.061 0.026 30.947
HMC 0.9 0.382 0.041 0.017 19.733
HMC 0.95 0.317 0.034 0.010 26.975
HMC 0.99 0.124 0.027 0.008 12.901
SMC 0.0 0.072 0.063 0.026 0.348
SMC 0.3 0.060 0.064 0.028 -0.125
SMC 0.5 0.053 0.061 0.026 -0.306
SMC 0.9 0.037 0.041 0.017 -0.188
SMC 0.95 0.033 0.034 0.010 -0.045
SMC 0.99 0.029 0.027 0.008 0.345
Metro 0.0 0.407 0.063 0.026 13.329
Metro 0.3 0.368 0.064 0.028 10.841
Metro 0.5 0.362 0.061 0.026 11.675
Metro 0.9 0.162 0.041 0.017 7.031
Metro 0.95 0.162 0.034 0.010 12.258
Metro 0.99 0.142 0.027 0.008 15.257
DEMetro_Z 0.0 0.470 0.063 0.026 15.762
DEMetro_Z 0.3 0.556 0.064 0.028 17.545
DEMetro_Z 0.5 0.459 0.061 0.026 15.416
DEMetro_Z 0.9 0.292 0.041 0.017 14.535
DEMetro_Z 0.95 0.151 0.034 0.010 11.225
DEMetro_Z 0.99 0.089 0.027 0.008 8.289
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 6.986 1.09e-07 36.428
HMC 0.3 7.094 8.17e-08 29.091
HMC 0.5 7.034 9.53e-08 26.839
HMC 0.9 7.587 2.15e-08 19.059
HMC 0.95 8.138 5.35e-09 24.242
HMC 0.99 7.024 9.05e-08 13.239
SMC 0.0 0.965 0.339 0.262
SMC 0.3 -0.288 0.775 -0.066
SMC 0.5 -1.427 0.16 -0.307
SMC 0.9 -0.689 0.494 -0.140
SMC 0.95 -0.382 0.704 -0.087
SMC 0.99 1.155 0.253 0.302
Metro 0.0 6.968 1.05e-07 12.854
Metro 0.3 6.442 4.24e-07 10.419
Metro 0.5 5.441 6.98e-06 9.826
Metro 0.9 6.639 1.94e-07 6.268
Metro 0.95 8.122 4.1e-09 9.518
Metro 0.99 8.228 3.67e-09 12.917
DEMetro_Z 0.0 5.966 1.68e-06 15.121
DEMetro_Z 0.3 6.211 8.62e-07 17.043
DEMetro_Z 0.5 6.074 1.23e-06 13.436
DEMetro_Z 0.9 6.640 2.61e-07 14.557
DEMetro_Z 0.95 6.305 6.11e-07 9.685
DEMetro_Z 0.99 8.259 2.37e-09 7.876
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 5.939 1.89e-06 1.084
DEMetro_Z_vs_SMC 0.3 6.268 7.66e-07 1.144
DEMetro_Z_vs_SMC 0.5 6.178 9.79e-07 1.128
DEMetro_Z_vs_SMC 0.9 6.662 2.64e-07 1.216
DEMetro_Z_vs_SMC 0.95 6.339 6.31e-07 1.157
DEMetro_Z_vs_SMC 0.99 8.166 5.28e-09 1.491
HMC_vs_Metro 0.0 4.091 0.000312 0.747
HMC_vs_Metro 0.3 4.476 0.000108 0.817
HMC_vs_Metro 0.5 4.123 0.000286 0.753
HMC_vs_Metro 0.9 5.057 2.17e-05 0.923
HMC_vs_Metro 0.95 4.925 3.13e-05 0.899
HMC_vs_Metro 0.99 0.125 0.902 0.023
Metro_vs_DEMetro_Z 0.0 -0.742 0.464 -0.135
Metro_vs_DEMetro_Z 0.3 -1.795 0.083 -0.328
Metro_vs_DEMetro_Z 0.5 -1.356 0.185 -0.248
Metro_vs_DEMetro_Z 0.9 -3.530 0.00141 -0.644
Metro_vs_DEMetro_Z 0.95 -0.087 0.931 -0.016
Metro_vs_DEMetro_Z 0.99 3.113 0.00414 0.568
HMC_vs_SMC 0.0 6.855 1.57e-07 1.252
HMC_vs_SMC 0.3 7.007 1.05e-07 1.279
HMC_vs_SMC 0.5 7.109 8.01e-08 1.298
HMC_vs_SMC 0.9 7.626 2.08e-08 1.392
HMC_vs_SMC 0.95 8.240 4.38e-09 1.504
HMC_vs_SMC 0.99 6.880 1.47e-07 1.256
Metro_vs_SMC 0.0 6.714 2.29e-07 1.226
Metro_vs_SMC 0.3 6.368 5.83e-07 1.163
Metro_vs_SMC 0.5 5.575 5.14e-06 1.018
Metro_vs_SMC 0.9 6.974 1.15e-07 1.273
Metro_vs_SMC 0.95 8.011 7.79e-09 1.463
Metro_vs_SMC 0.99 8.084 6.48e-09 1.476
HMC_vs_DEMetro_Z 0.0 3.509 0.00149 0.641
HMC_vs_DEMetro_Z 0.3 2.396 0.0232 0.437
HMC_vs_DEMetro_Z 0.5 3.142 0.00385 0.574
HMC_vs_DEMetro_Z 0.9 1.339 0.191 0.244
HMC_vs_DEMetro_Z 0.95 3.908 0.000514 0.713
HMC_vs_DEMetro_Z 0.99 2.664 0.0125 0.486
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.243 0.013 0.006 36.428
HMC 0.3 0.230 0.013 0.007 29.091
HMC 0.5 0.227 0.013 0.008 26.839
HMC 0.9 0.149 0.013 0.007 19.059
HMC 0.95 0.154 0.013 0.006 24.242
HMC 0.99 0.078 0.013 0.005 13.239
SMC 0.0 0.014 0.013 0.006 0.262
SMC 0.3 0.012 0.013 0.007 -0.066
SMC 0.5 0.011 0.013 0.008 -0.307
SMC 0.9 0.012 0.013 0.007 -0.140
SMC 0.95 0.013 0.013 0.006 -0.087
SMC 0.99 0.015 0.013 0.005 0.302
Metro 0.0 0.094 0.013 0.006 12.854
Metro 0.3 0.091 0.013 0.007 10.419
Metro 0.5 0.092 0.013 0.008 9.826
Metro 0.9 0.058 0.013 0.007 6.268
Metro 0.95 0.068 0.013 0.006 9.518
Metro 0.99 0.076 0.013 0.005 12.917
DEMetro_Z 0.0 0.108 0.013 0.006 15.121
DEMetro_Z 0.3 0.140 0.013 0.007 17.043
DEMetro_Z 0.5 0.121 0.013 0.008 13.436
DEMetro_Z 0.9 0.117 0.013 0.007 14.557
DEMetro_Z 0.95 0.069 0.013 0.006 9.685
DEMetro_Z 0.99 0.052 0.013 0.005 7.876
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 11.346 3.37e-12 57.460
HMC 0.3 12.909 1.42e-13 53.861
HMC 0.5 7.731 1.56e-08 37.836
HMC 0.9 7.976 8.11e-09 24.837
HMC 0.95 10.695 1.31e-11 35.737
HMC 0.99 8.668 1.21e-09 13.511
SMC 0.0 0.426 0.671 0.111
SMC 0.3 -0.311 0.757 -0.075
SMC 0.5 -1.215 0.23 -0.269
SMC 0.9 1.001 0.321 0.241
SMC 0.95 -0.985 0.329 -0.256
SMC 0.99 0.626 0.534 0.154
Metro 0.0 5.766 2.94e-06 16.036
Metro 0.3 6.441 4.35e-07 11.487
Metro 0.5 5.595 4.49e-06 9.327
Metro 0.9 6.169 8.32e-07 7.516
Metro 0.95 9.405 9.9e-11 7.719
Metro 0.99 4.310 0.000166 8.245
DEMetro_Z 0.0 4.539 8.86e-05 9.585
DEMetro_Z 0.3 3.104 0.00419 6.288
DEMetro_Z 0.5 3.141 0.00383 7.865
DEMetro_Z 0.9 3.333 0.00234 8.315
DEMetro_Z 0.95 3.818 0.000641 7.938
DEMetro_Z 0.99 4.295 0.000158 4.043
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 8.485 2.38e-09 1.549
HMC_vs_DEMetro_Z 0.3 10.849 1.01e-11 1.981
HMC_vs_DEMetro_Z 0.5 5.225 1.36e-05 0.954
HMC_vs_DEMetro_Z 0.9 4.131 0.00028 0.754
HMC_vs_DEMetro_Z 0.95 6.603 3.09e-07 1.206
HMC_vs_DEMetro_Z 0.99 5.725 3.39e-06 1.045
Metro_vs_SMC 0.0 5.658 4.09e-06 1.033
Metro_vs_SMC 0.3 6.559 3.48e-07 1.197
Metro_vs_SMC 0.5 5.733 3.32e-06 1.047
Metro_vs_SMC 0.9 5.886 2.18e-06 1.075
Metro_vs_SMC 0.95 9.609 1.62e-10 1.754
Metro_vs_SMC 0.99 4.346 0.000155 0.794
Metro_vs_DEMetro_Z 0.0 2.101 0.0444 0.384
Metro_vs_DEMetro_Z 0.3 1.824 0.0785 0.333
Metro_vs_DEMetro_Z 0.5 0.477 0.637 0.087
Metro_vs_DEMetro_Z 0.9 -0.268 0.79 -0.049
Metro_vs_DEMetro_Z 0.95 -0.099 0.922 -0.018
Metro_vs_DEMetro_Z 0.99 1.928 0.0637 0.352
HMC_vs_Metro 0.0 7.463 3.17e-08 1.363
HMC_vs_Metro 0.3 8.870 9.32e-10 1.619
HMC_vs_Metro 0.5 5.276 1.18e-05 0.963
HMC_vs_Metro 0.9 4.718 5.56e-05 0.861
HMC_vs_Metro 0.95 7.865 1.13e-08 1.436
HMC_vs_Metro 0.99 2.702 0.0114 0.493
HMC_vs_SMC 0.0 11.274 4.06e-12 2.058
HMC_vs_SMC 0.3 12.985 1.3e-13 2.371
HMC_vs_SMC 0.5 7.832 1.23e-08 1.430
HMC_vs_SMC 0.9 7.911 1e-08 1.444
HMC_vs_SMC 0.95 10.704 1.38e-11 1.954
HMC_vs_SMC 0.99 8.429 2.74e-09 1.539
DEMetro_Z_vs_SMC 0.0 4.430 0.000123 0.809
DEMetro_Z_vs_SMC 0.3 3.219 0.00316 0.588
DEMetro_Z_vs_SMC 0.5 3.234 0.00304 0.590
DEMetro_Z_vs_SMC 0.9 3.280 0.0027 0.599
DEMetro_Z_vs_SMC 0.95 3.870 0.000569 0.707
DEMetro_Z_vs_SMC 0.99 4.052 0.000348 0.740
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 1.988 0.052 0.034 57.460
HMC 0.3 2.015 0.054 0.036 53.861
HMC 0.5 1.392 0.051 0.035 37.836
HMC 0.9 0.583 0.030 0.022 24.837
HMC 0.95 0.563 0.023 0.015 35.737
HMC 0.99 0.172 0.018 0.011 13.511
SMC 0.0 0.056 0.052 0.034 0.111
SMC 0.3 0.051 0.054 0.036 -0.075
SMC 0.5 0.041 0.051 0.035 -0.269
SMC 0.9 0.035 0.030 0.022 0.241
SMC 0.95 0.020 0.023 0.015 -0.256
SMC 0.99 0.020 0.018 0.011 0.154
Metro 0.0 0.592 0.052 0.034 16.036
Metro 0.3 0.472 0.054 0.036 11.487
Metro 0.5 0.381 0.051 0.035 9.327
Metro 0.9 0.197 0.030 0.022 7.516
Metro 0.95 0.140 0.023 0.015 7.719
Metro 0.99 0.112 0.018 0.011 8.245
DEMetro_Z 0.0 0.375 0.052 0.034 9.585
DEMetro_Z 0.3 0.283 0.054 0.036 6.288
DEMetro_Z 0.5 0.330 0.051 0.035 7.865
DEMetro_Z 0.9 0.215 0.030 0.022 8.315
DEMetro_Z 0.95 0.143 0.023 0.015 7.938
DEMetro_Z 0.99 0.064 0.018 0.011 4.043
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 8.163 5.29e-09 91.927
HMC 0.3 9.313 3.22e-10 100.809
HMC 0.5 6.142 1.07e-06 52.283
HMC 0.9 4.830 4.05e-05 23.475
HMC 0.95 6.569 3.21e-07 15.943
HMC 0.99 6.065 6.73e-07 3.754
SMC 0.0 0.153 0.879 0.044
SMC 0.3 0.814 0.419 0.220
SMC 0.5 -0.522 0.604 -0.127
SMC 0.9 0.864 0.391 0.271
SMC 0.95 0.261 0.795 0.063
SMC 0.99 0.365 0.717 0.098
Metro 0.0 2.987 0.00566 11.064
Metro 0.3 4.636 6.64e-05 7.847
Metro 0.5 3.675 0.000911 4.339
Metro 0.9 6.941 8.98e-08 7.240
Metro 0.95 6.204 5.42e-07 4.539
Metro 0.99 7.109 5.48e-08 7.114
DEMetro_Z 0.0 3.253 0.00284 5.195
DEMetro_Z 0.3 2.467 0.0197 6.386
DEMetro_Z 0.5 1.851 0.0743 6.836
DEMetro_Z 0.9 2.672 0.0122 9.034
DEMetro_Z 0.95 2.761 0.00969 3.310
DEMetro_Z 0.99 5.435 3.59e-06 2.788
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 8.158 5.38e-09 1.489
HMC_vs_SMC 0.3 9.283 3.47e-10 1.695
HMC_vs_SMC 0.5 6.148 1.06e-06 1.122
HMC_vs_SMC 0.9 4.787 4.58e-05 0.874
HMC_vs_SMC 0.95 6.622 2.94e-07 1.209
HMC_vs_SMC 0.99 5.692 3.72e-06 1.039
Metro_vs_DEMetro_Z 0.0 1.576 0.126 0.288
Metro_vs_DEMetro_Z 0.3 0.480 0.635 0.088
Metro_vs_DEMetro_Z 0.5 -0.628 0.535 -0.115
Metro_vs_DEMetro_Z 0.9 -0.483 0.632 -0.088
Metro_vs_DEMetro_Z 0.95 0.792 0.435 0.145
Metro_vs_DEMetro_Z 0.99 4.006 0.000394 0.731
HMC_vs_Metro 0.0 7.098 8.25e-08 1.296
HMC_vs_Metro 0.3 8.246 4.32e-09 1.506
HMC_vs_Metro 0.5 5.524 5.93e-06 1.008
HMC_vs_Metro 0.9 3.491 0.00156 0.637
HMC_vs_Metro 0.95 4.634 7e-05 0.846
HMC_vs_Metro 0.99 -2.570 0.0156 -0.469
HMC_vs_DEMetro_Z 0.0 7.446 3.32e-08 1.359
HMC_vs_DEMetro_Z 0.3 8.622 1.7e-09 1.574
HMC_vs_DEMetro_Z 0.5 4.591 7.89e-05 0.838
HMC_vs_DEMetro_Z 0.9 2.465 0.0198 0.450
HMC_vs_DEMetro_Z 0.95 4.330 0.000162 0.791
HMC_vs_DEMetro_Z 0.99 1.180 0.247 0.215
Metro_vs_SMC 0.0 2.974 0.00587 0.543
Metro_vs_SMC 0.3 4.508 9.93e-05 0.823
Metro_vs_SMC 0.5 3.733 0.000821 0.682
Metro_vs_SMC 0.9 6.463 4.52e-07 1.180
Metro_vs_SMC 0.95 6.458 4.57e-07 1.179
Metro_vs_SMC 0.99 7.098 8.25e-08 1.296
DEMetro_Z_vs_SMC 0.0 3.268 0.00279 0.597
DEMetro_Z_vs_SMC 0.3 2.333 0.0268 0.426
DEMetro_Z_vs_SMC 0.5 1.919 0.0649 0.350
DEMetro_Z_vs_SMC 0.9 2.569 0.0156 0.469
DEMetro_Z_vs_SMC 0.95 2.701 0.0114 0.493
DEMetro_Z_vs_SMC 0.99 5.197 1.47e-05 0.949
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 6.800 0.108 0.073 91.927
HMC 0.3 6.631 0.096 0.065 100.809
HMC 0.5 3.973 0.100 0.074 52.283
HMC 0.9 0.681 0.049 0.027 23.475
HMC 0.95 0.533 0.047 0.030 15.943
HMC 0.99 0.091 0.028 0.017 3.754
SMC 0.0 0.112 0.108 0.073 0.044
SMC 0.3 0.110 0.096 0.065 0.220
SMC 0.5 0.091 0.100 0.074 -0.127
SMC 0.9 0.056 0.049 0.027 0.271
SMC 0.95 0.049 0.047 0.030 0.063
SMC 0.99 0.030 0.028 0.017 0.098
Metro 0.0 0.914 0.108 0.073 11.064
Metro 0.3 0.605 0.096 0.065 7.847
Metro 0.5 0.422 0.100 0.074 4.339
Metro 0.9 0.244 0.049 0.027 7.240
Metro 0.95 0.186 0.047 0.030 4.539
Metro 0.99 0.147 0.028 0.017 7.114
DEMetro_Z 0.0 0.487 0.108 0.073 5.195
DEMetro_Z 0.3 0.510 0.096 0.065 6.386
DEMetro_Z 0.5 0.607 0.100 0.074 6.836
DEMetro_Z 0.9 0.292 0.049 0.027 9.034
DEMetro_Z 0.95 0.148 0.047 0.030 3.310
DEMetro_Z 0.99 0.075 0.028 0.017 2.788
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 11.258 4.09e-12 64.666
HMC 0.3 12.261 5.16e-13 62.402
HMC 0.5 7.774 1.41e-08 45.987
HMC 0.9 7.790 1.32e-08 28.731
HMC 0.95 10.456 2.28e-11 45.343
HMC 0.99 8.428 2.43e-09 17.599
SMC 0.0 0.567 0.573 0.151
SMC 0.3 -0.275 0.784 -0.064
SMC 0.5 -1.356 0.181 -0.300
SMC 0.9 0.438 0.663 0.101
SMC 0.95 -0.650 0.518 -0.154
SMC 0.99 1.160 0.251 0.307
Metro 0.0 5.591 4.82e-06 18.596
Metro 0.3 6.409 4.85e-07 13.229
Metro 0.5 5.567 4.99e-06 11.444
Metro 0.9 7.494 2.24e-08 9.463
Metro 0.95 11.137 2.24e-12 10.941
Metro 0.99 5.768 2.89e-06 13.867
DEMetro_Z 0.0 4.695 5.77e-05 11.463
DEMetro_Z 0.3 3.419 0.00186 7.688
DEMetro_Z 0.5 3.407 0.00193 10.084
DEMetro_Z 0.9 3.718 0.000846 10.080
DEMetro_Z 0.95 4.205 0.000225 10.674
DEMetro_Z 0.99 6.111 9.17e-07 6.382
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 1.991 0.056 0.363
Metro_vs_DEMetro_Z 0.3 1.730 0.0943 0.316
Metro_vs_DEMetro_Z 0.5 0.367 0.716 0.067
Metro_vs_DEMetro_Z 0.9 -0.191 0.85 -0.035
Metro_vs_DEMetro_Z 0.95 0.096 0.924 0.018
Metro_vs_DEMetro_Z 0.99 2.751 0.0101 0.502
DEMetro_Z_vs_SMC 0.0 4.545 8.97e-05 0.830
DEMetro_Z_vs_SMC 0.3 3.519 0.00145 0.642
DEMetro_Z_vs_SMC 0.5 3.512 0.00148 0.641
DEMetro_Z_vs_SMC 0.9 3.733 0.000823 0.681
DEMetro_Z_vs_SMC 0.95 4.221 0.000219 0.771
DEMetro_Z_vs_SMC 0.99 5.769 3e-06 1.053
HMC_vs_DEMetro_Z 0.0 8.225 4.54e-09 1.502
HMC_vs_DEMetro_Z 0.3 10.141 4.79e-11 1.852
HMC_vs_DEMetro_Z 0.5 5.189 1.5e-05 0.947
HMC_vs_DEMetro_Z 0.9 4.128 0.000283 0.754
HMC_vs_DEMetro_Z 0.95 6.462 4.52e-07 1.180
HMC_vs_DEMetro_Z 0.99 5.093 1.96e-05 0.930
HMC_vs_Metro 0.0 7.148 7.24e-08 1.305
HMC_vs_Metro 0.3 8.323 3.56e-09 1.520
HMC_vs_Metro 0.5 5.265 1.22e-05 0.961
HMC_vs_Metro 0.9 4.586 8.01e-05 0.837
HMC_vs_Metro 0.95 7.350 4.26e-08 1.342
HMC_vs_Metro 0.99 1.371 0.181 0.250
HMC_vs_SMC 0.0 11.210 4.65e-12 2.047
HMC_vs_SMC 0.3 12.266 5.31e-13 2.239
HMC_vs_SMC 0.5 7.866 1.13e-08 1.436
HMC_vs_SMC 0.9 7.780 1.4e-08 1.421
HMC_vs_SMC 0.95 10.524 2.04e-11 1.921
HMC_vs_SMC 0.99 8.274 4.03e-09 1.511
Metro_vs_SMC 0.0 5.485 6.59e-06 1.001
Metro_vs_SMC 0.3 6.485 4.25e-07 1.184
Metro_vs_SMC 0.5 5.706 3.58e-06 1.042
Metro_vs_SMC 0.9 7.277 5.15e-08 1.329
Metro_vs_SMC 0.95 11.561 2.23e-12 2.111
Metro_vs_SMC 0.99 5.815 2.65e-06 1.062
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 1.733 0.063 0.026 64.666
HMC 0.3 1.813 0.064 0.028 62.402
HMC 0.5 1.248 0.061 0.026 45.987
HMC 0.9 0.538 0.041 0.017 28.731
HMC 0.95 0.509 0.034 0.010 45.343
HMC 0.99 0.160 0.027 0.008 17.599
SMC 0.0 0.067 0.063 0.026 0.151
SMC 0.3 0.062 0.064 0.028 -0.064
SMC 0.5 0.054 0.061 0.026 -0.300
SMC 0.9 0.042 0.041 0.017 0.101
SMC 0.95 0.032 0.034 0.010 -0.154
SMC 0.99 0.029 0.027 0.008 0.307
Metro 0.0 0.543 0.063 0.026 18.596
Metro 0.3 0.435 0.064 0.028 13.229
Metro 0.5 0.357 0.061 0.026 11.444
Metro 0.9 0.204 0.041 0.017 9.463
Metro 0.95 0.148 0.034 0.010 10.941
Metro 0.99 0.131 0.027 0.008 13.867
DEMetro_Z 0.0 0.359 0.063 0.026 11.463
DEMetro_Z 0.3 0.279 0.064 0.028 7.688
DEMetro_Z 0.5 0.321 0.061 0.026 10.084
DEMetro_Z 0.9 0.215 0.041 0.017 10.080
DEMetro_Z 0.95 0.146 0.034 0.010 10.674
DEMetro_Z 0.99 0.075 0.027 0.008 6.382
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 11.419 2.92e-12 65.989
HMC 0.3 12.890 1.49e-13 58.765
HMC 0.5 7.596 2.22e-08 41.761
HMC 0.9 7.719 1.59e-08 28.964
HMC 0.95 10.140 4.59e-11 40.067
HMC 0.99 9.221 3.44e-10 18.440
SMC 0.0 0.124 0.902 0.032
SMC 0.3 -0.544 0.589 -0.125
SMC 0.5 -1.522 0.134 -0.333
SMC 0.9 0.674 0.503 0.150
SMC 0.95 -0.375 0.709 -0.088
SMC 0.99 1.529 0.132 0.413
Metro 0.0 5.643 4.16e-06 18.023
Metro 0.3 6.399 4.94e-07 12.330
Metro 0.5 5.479 6.23e-06 9.337
Metro 0.9 7.853 8.02e-09 8.791
Metro 0.95 10.672 4.42e-12 8.698
Metro 0.99 7.229 4.95e-08 11.082
DEMetro_Z 0.0 4.647 6.58e-05 10.863
DEMetro_Z 0.3 3.287 0.00262 6.946
DEMetro_Z 0.5 3.130 0.00394 8.211
DEMetro_Z 0.9 3.492 0.00154 9.838
DEMetro_Z 0.95 3.862 0.000573 9.192
DEMetro_Z 0.99 5.325 8.67e-06 5.698
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 4.561 8.58e-05 0.833
DEMetro_Z_vs_SMC 0.3 3.401 0.00198 0.621
DEMetro_Z_vs_SMC 0.5 3.260 0.00284 0.595
DEMetro_Z_vs_SMC 0.9 3.486 0.00158 0.636
DEMetro_Z_vs_SMC 0.95 3.857 0.000588 0.704
DEMetro_Z_vs_SMC 0.99 4.883 3.51e-05 0.892
HMC_vs_Metro 0.0 7.421 3.54e-08 1.355
HMC_vs_Metro 0.3 8.872 9.27e-10 1.620
HMC_vs_Metro 0.5 5.436 7.56e-06 0.992
HMC_vs_Metro 0.9 4.821 4.17e-05 0.880
HMC_vs_Metro 0.95 7.456 3.24e-08 1.361
HMC_vs_Metro 0.99 3.335 0.00235 0.609
Metro_vs_DEMetro_Z 0.0 2.036 0.051 0.372
Metro_vs_DEMetro_Z 0.3 1.802 0.0819 0.329
Metro_vs_DEMetro_Z 0.5 0.353 0.727 0.064
Metro_vs_DEMetro_Z 0.9 -0.324 0.748 -0.059
Metro_vs_DEMetro_Z 0.95 -0.192 0.849 -0.035
Metro_vs_DEMetro_Z 0.99 2.660 0.0126 0.486
HMC_vs_SMC 0.0 11.394 3.16e-12 2.080
HMC_vs_SMC 0.3 12.964 1.35e-13 2.367
HMC_vs_SMC 0.5 7.699 1.73e-08 1.406
HMC_vs_SMC 0.9 7.715 1.66e-08 1.409
HMC_vs_SMC 0.95 10.201 4.19e-11 1.862
HMC_vs_SMC 0.99 9.048 6.07e-10 1.652
Metro_vs_SMC 0.0 5.584 5.02e-06 1.019
Metro_vs_SMC 0.3 6.556 3.51e-07 1.197
Metro_vs_SMC 0.5 5.635 4.35e-06 1.029
Metro_vs_SMC 0.9 7.676 1.83e-08 1.401
Metro_vs_SMC 0.95 11.457 2.77e-12 2.092
Metro_vs_SMC 0.99 7.139 7.4e-08 1.303
HMC_vs_DEMetro_Z 0.0 8.550 2.03e-09 1.561
HMC_vs_DEMetro_Z 0.3 10.915 8.72e-12 1.993
HMC_vs_DEMetro_Z 0.5 5.245 1.28e-05 0.958
HMC_vs_DEMetro_Z 0.9 4.106 0.0003 0.750
HMC_vs_DEMetro_Z 0.95 6.174 9.88e-07 1.127
HMC_vs_DEMetro_Z 0.99 6.232 8.43e-07 1.138
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.430 0.013 0.006 65.989
HMC 0.3 0.451 0.013 0.007 58.765
HMC 0.5 0.346 0.013 0.008 41.761
HMC 0.9 0.220 0.013 0.007 28.964
HMC 0.95 0.246 0.013 0.006 40.067
HMC 0.99 0.103 0.013 0.005 18.440
SMC 0.0 0.013 0.013 0.006 0.032
SMC 0.3 0.012 0.013 0.007 -0.125
SMC 0.5 0.011 0.013 0.008 -0.333
SMC 0.9 0.014 0.013 0.007 0.150
SMC 0.95 0.013 0.013 0.006 -0.088
SMC 0.99 0.015 0.013 0.005 0.413
Metro 0.0 0.127 0.013 0.006 18.023
Metro 0.3 0.105 0.013 0.007 12.330
Metro 0.5 0.088 0.013 0.008 9.337
Metro 0.9 0.076 0.013 0.007 8.791
Metro 0.95 0.064 0.013 0.006 8.698
Metro 0.99 0.067 0.013 0.005 11.082
DEMetro_Z 0.0 0.081 0.013 0.006 10.863
DEMetro_Z 0.3 0.065 0.013 0.007 6.946
DEMetro_Z 0.5 0.079 0.013 0.008 8.211
DEMetro_Z 0.9 0.083 0.013 0.007 9.838
DEMetro_Z 0.95 0.066 0.013 0.006 9.192
DEMetro_Z 0.99 0.041 0.013 0.005 5.698
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Mode Transitions (scatter)
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Forest & Ridge Plots
Pooled
0.0 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.9 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.95 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.99 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
0.0 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.9 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.95 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.99 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
0.0
0.3
0.5
0.9
0.95
0.99
Chain
0.0
0.3
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two_attr_dim

▼

Vary_Dimension_with_high_correlation (MvNormal, dimension, 30 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 3.530 0.000926 1.233
HMC 3 3.489 0.000986 1.083
HMC 5 3.683 0.000733 1.915
HMC 8 2.973 0.00506 1.414
HMC 15 5.263 7.7e-06 3.335
HMC 30 5.150 1.48e-05 6.259
SMC 2 -0.380 0.706 -0.109
SMC 3 -1.091 0.281 -0.231
SMC 5 0.210 0.834 0.058
SMC 8 -0.236 0.814 -0.056
SMC 15 -0.825 0.413 -0.211
SMC 30 -2.551 0.0135 -0.736
Metro 2 4.755 4.65e-05 6.649
Metro 3 6.731 1.79e-07 8.715
Metro 5 7.392 3.58e-08 18.868
Metro 8 7.939 8.63e-09 19.442
Metro 15 6.965 1.15e-07 28.729
Metro 30 8.038 7.15e-09 42.409
DEMetro_Z 2 3.226 0.0026 1.625
DEMetro_Z 3 5.663 4.01e-06 43.233
DEMetro_Z 5 7.124 7.71e-08 620.224
DEMetro_Z 8 14.288 1.17e-14 351.974
DEMetro_Z 15 22.828 4.4e-20 458.820
DEMetro_Z 30 44.028 4.03e-28 584.440
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -0.661 0.514 -0.121
HMC_vs_DEMetro_Z 1 -5.542 5.63e-06 -1.012
HMC_vs_DEMetro_Z 2 -7.108 8.03e-08 -1.298
HMC_vs_DEMetro_Z 3 -14.302 1.14e-14 -2.611
HMC_vs_DEMetro_Z 4 -22.559 6.14e-20 -4.119
HMC_vs_DEMetro_Z 5 -43.280 6.69e-28 -7.902
Metro_vs_SMC 0 4.711 5.66e-05 0.860
Metro_vs_SMC 1 6.950 1.22e-07 1.269
Metro_vs_SMC 2 7.350 4.27e-08 1.342
Metro_vs_SMC 3 7.950 9.1e-09 1.451
Metro_vs_SMC 4 7.193 6.43e-08 1.313
Metro_vs_SMC 5 8.071 6.7e-09 1.473
Metro_vs_DEMetro_Z 0 3.467 0.00166 0.633
Metro_vs_DEMetro_Z 1 -4.373 0.000144 -0.798
Metro_vs_DEMetro_Z 2 -6.940 1.25e-07 -1.267
Metro_vs_DEMetro_Z 3 -13.455 5.36e-14 -2.456
Metro_vs_DEMetro_Z 4 -21.275 3.06e-19 -3.884
Metro_vs_DEMetro_Z 5 -40.251 5.31e-27 -7.349
HMC_vs_Metro 0 -4.019 0.00038 -0.734
HMC_vs_Metro 1 -5.979 1.69e-06 -1.092
HMC_vs_Metro 2 -6.985 1.11e-07 -1.275
HMC_vs_Metro 3 -6.992 1.09e-07 -1.277
HMC_vs_Metro 4 -5.877 2.23e-06 -1.073
HMC_vs_Metro 5 -6.327 6.52e-07 -1.155
HMC_vs_SMC 0 3.274 0.00275 0.598
HMC_vs_SMC 1 4.092 0.000312 0.747
HMC_vs_SMC 2 4.434 0.000122 0.810
HMC_vs_SMC 3 3.011 0.00536 0.550
HMC_vs_SMC 4 5.263 1.22e-05 0.961
HMC_vs_SMC 5 5.650 4.18e-06 1.031
DEMetro_Z_vs_SMC 0 3.353 0.00224 0.612
DEMetro_Z_vs_SMC 1 5.694 3.7e-06 1.040
DEMetro_Z_vs_SMC 2 7.125 7.68e-08 1.301
DEMetro_Z_vs_SMC 3 14.285 1.18e-14 2.608
DEMetro_Z_vs_SMC 4 22.839 4.37e-20 4.170
DEMetro_Z_vs_SMC 5 43.987 4.21e-28 8.031
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.037 0.022 0.012 1.233
HMC 3 0.036 0.019 0.016 1.083
HMC 5 0.036 0.017 0.010 1.915
HMC 8 0.039 0.019 0.014 1.414
HMC 15 0.060 0.019 0.012 3.335
HMC 30 0.093 0.024 0.011 6.259
SMC 2 0.020 0.022 0.012 -0.109
SMC 3 0.015 0.019 0.016 -0.231
SMC 5 0.017 0.017 0.010 0.058
SMC 8 0.018 0.019 0.014 -0.056
SMC 15 0.016 0.019 0.012 -0.211
SMC 30 0.016 0.024 0.011 -0.736
Metro 2 0.102 0.022 0.012 6.649
Metro 3 0.154 0.019 0.016 8.715
Metro 5 0.207 0.017 0.010 18.868
Metro 8 0.298 0.019 0.014 19.442
Metro 15 0.376 0.019 0.012 28.729
Metro 30 0.491 0.024 0.011 42.409
DEMetro_Z 2 0.041 0.022 0.012 1.625
DEMetro_Z 3 0.690 0.019 0.016 43.233
DEMetro_Z 5 6.255 0.017 0.010 620.224
DEMetro_Z 8 5.087 0.019 0.014 351.974
DEMetro_Z 15 5.722 0.019 0.012 458.820
DEMetro_Z 30 6.461 0.024 0.011 584.440
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 4.501 6.53e-05 2.349
HMC 3 2.978 0.00484 1.273
HMC 5 4.326 0.000115 2.395
HMC 8 3.909 0.000361 1.855
HMC 15 7.083 4.53e-08 5.418
HMC 30 5.044 1.73e-05 4.069
SMC 2 2.573 0.0135 0.983
SMC 3 -1.010 0.317 -0.256
SMC 5 -1.060 0.293 -0.269
SMC 8 0.312 0.756 0.072
SMC 15 1.344 0.185 0.443
SMC 30 -0.392 0.697 -0.091
Metro 2 6.559 2.9e-07 8.700
Metro 3 7.771 1.1e-08 10.117
Metro 5 9.192 3.41e-10 15.064
Metro 8 6.798 1.63e-07 11.794
Metro 15 6.469 4.37e-07 29.758
Metro 30 5.784 2.86e-06 26.944
DEMetro_Z 2 5.204 9.36e-06 3.370
DEMetro_Z 3 4.855 3.8e-05 965.993
DEMetro_Z 5 7.736 1.57e-08 7935.116
DEMetro_Z 8 12.065 7.95e-13 6074.478
DEMetro_Z 15 21.018 4.25e-19 10205.749
DEMetro_Z 30 41.377 2.42e-27 7838.341
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 2.443 0.0209 0.446
HMC_vs_SMC 1 3.268 0.00278 0.597
HMC_vs_SMC 2 5.006 2.5e-05 0.914
HMC_vs_SMC 3 3.862 0.000581 0.705
HMC_vs_SMC 4 6.466 4.48e-07 1.180
HMC_vs_SMC 5 5.216 1.39e-05 0.952
Metro_vs_DEMetro_Z 0 3.711 0.000872 0.678
Metro_vs_DEMetro_Z 1 -4.796 4.48e-05 -0.876
Metro_vs_DEMetro_Z 2 -7.721 1.63e-08 -1.410
Metro_vs_DEMetro_Z 3 -12.037 8.4e-13 -2.198
Metro_vs_DEMetro_Z 4 -20.953 4.63e-19 -3.825
Metro_vs_DEMetro_Z 5 -41.305 2.54e-27 -7.541
HMC_vs_Metro 0 -4.359 0.00015 -0.796
HMC_vs_Metro 1 -6.590 3.2e-07 -1.203
HMC_vs_Metro 2 -8.393 3e-09 -1.532
HMC_vs_Metro 3 -5.536 5.73e-06 -1.011
HMC_vs_Metro 4 -5.361 9.31e-06 -0.979
HMC_vs_Metro 5 -5.022 2.39e-05 -0.917
HMC_vs_DEMetro_Z 0 -1.471 0.152 -0.269
HMC_vs_DEMetro_Z 1 -4.845 3.9e-05 -0.885
HMC_vs_DEMetro_Z 2 -7.733 1.58e-08 -1.412
HMC_vs_DEMetro_Z 3 -12.061 8e-13 -2.202
HMC_vs_DEMetro_Z 4 -20.997 4.38e-19 -3.833
HMC_vs_DEMetro_Z 5 -41.328 2.5e-27 -7.545
Metro_vs_SMC 0 5.303 1.09e-05 0.968
Metro_vs_SMC 1 8.228 4.52e-09 1.502
Metro_vs_SMC 2 9.332 3.09e-10 1.704
Metro_vs_SMC 3 6.801 1.82e-07 1.242
Metro_vs_SMC 4 6.288 7.25e-07 1.148
Metro_vs_SMC 5 5.819 2.62e-06 1.062
DEMetro_Z_vs_SMC 0 3.209 0.00324 0.586
DEMetro_Z_vs_SMC 1 4.857 3.78e-05 0.887
DEMetro_Z_vs_SMC 2 7.736 1.57e-08 1.412
DEMetro_Z_vs_SMC 3 12.064 7.95e-13 2.203
DEMetro_Z_vs_SMC 4 21.017 4.26e-19 3.837
DEMetro_Z_vs_SMC 5 41.371 2.43e-27 7.553
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.045 0.019 0.011 2.349
HMC 3 0.054 0.030 0.019 1.273
HMC 5 0.065 0.028 0.015 2.395
HMC 8 0.059 0.026 0.018 1.855
HMC 15 0.094 0.024 0.013 5.418
HMC 30 0.117 0.029 0.022 4.069
SMC 2 0.030 0.019 0.011 0.983
SMC 3 0.025 0.030 0.019 -0.256
SMC 5 0.024 0.028 0.015 -0.269
SMC 8 0.027 0.026 0.018 0.072
SMC 15 0.030 0.024 0.013 0.443
SMC 30 0.027 0.029 0.022 -0.091
Metro 2 0.115 0.019 0.011 8.700
Metro 3 0.223 0.030 0.019 10.117
Metro 5 0.258 0.028 0.015 15.064
Metro 8 0.235 0.026 0.018 11.794
Metro 15 0.405 0.024 0.013 29.758
Metro 30 0.609 0.029 0.022 26.944
DEMetro_Z 2 0.056 0.019 0.011 3.370
DEMetro_Z 3 18.389 0.030 0.019 965.993
DEMetro_Z 5 120.893 0.028 0.015 7935.116
DEMetro_Z 8 107.824 0.026 0.018 6074.478
DEMetro_Z 15 130.735 0.024 0.013 10205.749
DEMetro_Z 30 168.762 0.029 0.022 7838.341
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 4.793 1.63e-05 1.678
HMC 3 4.638 2.54e-05 1.539
HMC 5 5.868 1.43e-06 4.243
HMC 8 4.768 2.86e-05 2.463
HMC 15 7.717 8.25e-09 6.211
HMC 30 7.656 1.53e-08 10.688
SMC 2 0.243 0.809 0.071
SMC 3 -1.697 0.0973 -0.340
SMC 5 0.519 0.606 0.167
SMC 8 -0.497 0.621 -0.128
SMC 15 0.345 0.731 0.100
SMC 30 -2.364 0.0215 -0.653
Metro 2 6.902 1.2e-07 10.863
Metro 3 10.446 1.45e-11 12.798
Metro 5 11.020 6.54e-12 40.437
Metro 8 9.681 1.27e-10 29.219
Metro 15 8.493 2.3e-09 50.176
Metro 30 11.465 2.66e-12 69.260
DEMetro_Z 2 6.482 1.39e-07 3.359
DEMetro_Z 3 8.585 1.85e-09 83.304
DEMetro_Z 5 12.943 1.41e-13 1833.818
DEMetro_Z 8 28.280 1.15e-22 956.499
DEMetro_Z 15 49.920 1.12e-29 1343.122
DEMetro_Z 30 74.499 1.11e-34 1562.633
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 4.765 4.88e-05 0.870
Metro_vs_DEMetro_Z 1 -7.048 9.42e-08 -1.287
Metro_vs_DEMetro_Z 2 -12.675 2.37e-13 -2.314
Metro_vs_DEMetro_Z 3 -27.604 2.27e-22 -5.040
Metro_vs_DEMetro_Z 4 -47.389 5e-29 -8.652
Metro_vs_DEMetro_Z 5 -70.084 6.5e-34 -12.795
DEMetro_Z_vs_SMC 0 5.699 3.65e-06 1.040
DEMetro_Z_vs_SMC 1 8.649 1.59e-09 1.579
DEMetro_Z_vs_SMC 2 12.940 1.42e-13 2.363
DEMetro_Z_vs_SMC 3 28.319 1.11e-22 5.170
DEMetro_Z_vs_SMC 4 49.969 1.09e-29 9.123
DEMetro_Z_vs_SMC 5 74.453 1.14e-34 13.593
HMC_vs_DEMetro_Z 0 -2.920 0.00671 -0.533
HMC_vs_DEMetro_Z 1 -8.396 2.97e-09 -1.533
HMC_vs_DEMetro_Z 2 -12.917 1.48e-13 -2.358
HMC_vs_DEMetro_Z 3 -28.146 1.32e-22 -5.139
HMC_vs_DEMetro_Z 4 -49.170 1.74e-29 -8.977
HMC_vs_DEMetro_Z 5 -73.883 1.42e-34 -13.489
HMC_vs_Metro 0 -6.133 1.11e-06 -1.120
HMC_vs_Metro 1 -9.165 4.59e-10 -1.673
HMC_vs_Metro 2 -10.211 4.1e-11 -1.864
HMC_vs_Metro 3 -8.575 1.91e-09 -1.566
HMC_vs_Metro 4 -7.265 5.33e-08 -1.326
HMC_vs_Metro 5 -9.032 6.31e-10 -1.649
HMC_vs_SMC 0 3.868 0.000571 0.706
HMC_vs_SMC 1 6.028 1.48e-06 1.101
HMC_vs_SMC 2 6.214 8.88e-07 1.134
HMC_vs_SMC 3 4.749 5.09e-05 0.867
HMC_vs_SMC 4 7.022 1.01e-07 1.282
HMC_vs_SMC 5 7.913 1e-08 1.445
Metro_vs_SMC 0 6.676 2.54e-07 1.219
Metro_vs_SMC 1 10.767 1.2e-11 1.966
Metro_vs_SMC 2 10.859 9.85e-12 1.983
Metro_vs_SMC 3 9.659 1.44e-10 1.763
Metro_vs_SMC 4 8.655 1.57e-09 1.580
Metro_vs_SMC 5 11.536 2.35e-12 2.106
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.041 0.027 0.008 1.678
HMC 3 0.044 0.028 0.011 1.539
HMC 5 0.043 0.023 0.005 4.243
HMC 8 0.046 0.025 0.008 2.463
HMC 15 0.065 0.024 0.007 6.211
HMC 30 0.098 0.028 0.007 10.688
SMC 2 0.028 0.027 0.008 0.071
SMC 3 0.024 0.028 0.011 -0.340
SMC 5 0.024 0.023 0.005 0.167
SMC 8 0.024 0.025 0.008 -0.128
SMC 15 0.024 0.024 0.007 0.100
SMC 30 0.023 0.028 0.007 -0.653
Metro 2 0.115 0.027 0.008 10.863
Metro 3 0.166 0.028 0.011 12.798
Metro 5 0.212 0.023 0.005 40.437
Metro 8 0.268 0.025 0.008 29.219
Metro 15 0.362 0.024 0.007 50.176
Metro 30 0.484 0.028 0.007 69.260
DEMetro_Z 2 0.054 0.027 0.008 3.359
DEMetro_Z 3 0.932 0.028 0.011 83.304
DEMetro_Z 5 8.574 0.023 0.005 1833.818
DEMetro_Z 8 7.987 0.025 0.008 956.499
DEMetro_Z 15 9.072 0.024 0.007 1343.122
DEMetro_Z 30 10.322 0.028 0.007 1562.633
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 3.937 0.000245 1.240
HMC 3 4.750 1.59e-05 1.473
HMC 5 5.299 7.55e-06 3.745
HMC 8 4.806 1.96e-05 1.980
HMC 15 8.207 1.42e-09 5.305
HMC 30 8.634 1.03e-09 9.340
SMC 2 -0.086 0.932 -0.024
SMC 3 -0.894 0.376 -0.193
SMC 5 0.445 0.658 0.145
SMC 8 -0.020 0.984 -0.005
SMC 15 0.375 0.709 0.103
SMC 30 -1.835 0.0716 -0.454
Metro 2 7.353 3.44e-08 10.333
Metro 3 11.022 3.08e-12 11.224
Metro 5 12.420 3.46e-13 35.650
Metro 8 10.783 9.72e-12 23.043
Metro 15 11.119 5.32e-12 41.830
Metro 30 14.180 1.31e-14 56.008
DEMetro_Z 2 6.353 1.83e-07 3.099
DEMetro_Z 3 12.823 6.91e-14 13.512
DEMetro_Z 5 33.890 6.55e-25 206.092
DEMetro_Z 8 56.453 1.02e-31 99.767
DEMetro_Z 15 59.059 3.7e-32 121.021
DEMetro_Z 30 97.598 1.05e-39 109.776
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 5.759 3.09e-06 1.051
DEMetro_Z_vs_SMC 1 13.044 1.16e-13 2.381
DEMetro_Z_vs_SMC 2 34.174 5.56e-25 6.239
DEMetro_Z_vs_SMC 3 55.759 4.7e-31 10.180
DEMetro_Z_vs_SMC 4 57.609 1.84e-31 10.518
DEMetro_Z_vs_SMC 5 94.237 1.26e-37 17.205
HMC_vs_Metro 0 -6.768 1.99e-07 -1.236
HMC_vs_Metro 1 -9.574 1.75e-10 -1.748
HMC_vs_Metro 2 -11.938 1.03e-12 -2.180
HMC_vs_Metro 3 -9.630 1.54e-10 -1.758
HMC_vs_Metro 4 -9.560 1.81e-10 -1.745
HMC_vs_Metro 5 -10.825 1.06e-11 -1.976
Metro_vs_DEMetro_Z 0 5.350 9.6e-06 0.977
Metro_vs_DEMetro_Z 1 -1.523 0.139 -0.278
Metro_vs_DEMetro_Z 2 -30.116 1.97e-23 -5.498
Metro_vs_DEMetro_Z 3 -27.832 1.8e-22 -5.081
Metro_vs_DEMetro_Z 4 -19.441 3.53e-18 -3.549
Metro_vs_DEMetro_Z 5 -12.821 1.79e-13 -2.341
HMC_vs_SMC 0 3.616 0.00112 0.660
HMC_vs_SMC 1 5.895 2.13e-06 1.076
HMC_vs_SMC 2 5.573 5.16e-06 1.018
HMC_vs_SMC 3 4.864 3.7e-05 0.888
HMC_vs_SMC 4 7.605 2.2e-08 1.389
HMC_vs_SMC 5 8.848 9.82e-10 1.615
Metro_vs_SMC 0 7.233 5.79e-08 1.321
Metro_vs_SMC 1 11.485 2.61e-12 2.097
Metro_vs_SMC 2 12.377 4.25e-13 2.260
Metro_vs_SMC 3 10.754 1.24e-11 1.963
Metro_vs_SMC 4 11.297 3.87e-12 2.062
Metro_vs_SMC 5 14.273 1.2e-14 2.606
HMC_vs_DEMetro_Z 0 -4.328 0.000163 -0.790
HMC_vs_DEMetro_Z 1 -11.326 3.64e-12 -2.068
HMC_vs_DEMetro_Z 2 -33.651 8.6e-25 -6.144
HMC_vs_DEMetro_Z 3 -57.570 1.87e-31 -10.511
HMC_vs_DEMetro_Z 4 -60.788 3.92e-32 -11.098
HMC_vs_DEMetro_Z 5 -65.217 5.18e-33 -11.907
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.020 0.014 0.005 1.240
HMC 3 0.026 0.015 0.007 1.473
HMC 5 0.026 0.013 0.003 3.745
HMC 8 0.027 0.014 0.006 1.980
HMC 15 0.039 0.014 0.005 5.305
HMC 30 0.063 0.016 0.005 9.340
SMC 2 0.014 0.014 0.005 -0.024
SMC 3 0.013 0.015 0.007 -0.193
SMC 5 0.013 0.013 0.003 0.145
SMC 8 0.014 0.014 0.006 -0.005
SMC 15 0.014 0.014 0.005 0.103
SMC 30 0.014 0.016 0.005 -0.454
Metro 2 0.065 0.014 0.005 10.333
Metro 3 0.098 0.015 0.007 11.224
Metro 5 0.135 0.013 0.003 35.650
Metro 8 0.163 0.014 0.006 23.043
Metro 15 0.214 0.014 0.005 41.830
Metro 30 0.299 0.016 0.005 56.008
DEMetro_Z 2 0.029 0.014 0.005 3.099
DEMetro_Z 3 0.115 0.015 0.007 13.512
DEMetro_Z 5 0.719 0.013 0.003 206.092
DEMetro_Z 8 0.657 0.014 0.006 99.767
DEMetro_Z 15 0.594 0.014 0.005 121.021
DEMetro_Z 30 0.571 0.016 0.005 109.776
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 1.338 0.188 0.521
HMC 3 1.149 0.255 0.341
HMC 5 5.449 3.61e-06 2.904
HMC 8 4.339 9.53e-05 1.975
HMC 15 3.368 0.00182 1.873
HMC 30 6.277 5.77e-07 6.666
SMC 2 -1.389 0.17 -0.351
SMC 3 -0.185 0.854 -0.045
SMC 5 -0.264 0.792 -0.072
SMC 8 -0.254 0.801 -0.059
SMC 15 0.157 0.876 0.044
SMC 30 -1.035 0.305 -0.291
Metro 2 6.022 1.37e-06 10.408
Metro 3 7.355 3.43e-08 10.378
Metro 5 7.699 1.66e-08 27.186
Metro 8 6.863 1.49e-07 23.958
Metro 15 6.816 1.72e-07 34.438
Metro 30 6.775 1.94e-07 68.745
DEMetro_Z 2 1.418 0.164 0.604
DEMetro_Z 3 4.377 0.00014 11.172
DEMetro_Z 5 6.421 5.05e-07 648.043
DEMetro_Z 8 7.676 1.83e-08 540.024
DEMetro_Z 15 28.788 6.97e-23 743.445
DEMetro_Z 30 36.403 9.23e-26 1011.243
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -0.154 0.879 -0.028
HMC_vs_DEMetro_Z 1 -4.117 0.000291 -0.752
HMC_vs_DEMetro_Z 2 -6.382 5.62e-07 -1.165
HMC_vs_DEMetro_Z 3 -7.640 2.01e-08 -1.395
HMC_vs_DEMetro_Z 4 -28.892 6.32e-23 -5.275
HMC_vs_DEMetro_Z 5 -36.341 9.73e-26 -6.635
Metro_vs_SMC 0 6.246 8.13e-07 1.140
Metro_vs_SMC 1 7.388 3.86e-08 1.349
Metro_vs_SMC 2 7.767 1.45e-08 1.418
Metro_vs_SMC 3 6.831 1.68e-07 1.247
Metro_vs_SMC 4 6.878 1.48e-07 1.256
Metro_vs_SMC 5 6.823 1.71e-07 1.246
Metro_vs_DEMetro_Z 0 5.570 5.21e-06 1.017
Metro_vs_DEMetro_Z 1 -0.263 0.795 -0.048
Metro_vs_DEMetro_Z 2 -6.179 9.75e-07 -1.128
Metro_vs_DEMetro_Z 3 -7.237 5.72e-08 -1.321
Metro_vs_DEMetro_Z 4 -25.596 1.87e-21 -4.673
Metro_vs_DEMetro_Z 5 -35.147 2.51e-25 -6.417
HMC_vs_Metro 0 -5.940 1.88e-06 -1.084
HMC_vs_Metro 1 -7.254 5.47e-08 -1.324
HMC_vs_Metro 2 -6.767 1.99e-07 -1.235
HMC_vs_Metro 3 -6.398 5.38e-07 -1.168
HMC_vs_Metro 4 -6.148 1.06e-06 -1.123
HMC_vs_Metro 5 -6.241 8.23e-07 -1.140
HMC_vs_SMC 0 2.536 0.0169 0.463
HMC_vs_SMC 1 1.400 0.172 0.256
HMC_vs_SMC 2 5.643 4.26e-06 1.030
HMC_vs_SMC 3 4.640 6.88e-05 0.847
HMC_vs_SMC 4 3.085 0.00444 0.563
HMC_vs_SMC 5 6.723 2.24e-07 1.227
DEMetro_Z_vs_SMC 0 2.202 0.0357 0.402
DEMetro_Z_vs_SMC 1 4.354 0.000152 0.795
DEMetro_Z_vs_SMC 2 6.426 4.98e-07 1.173
DEMetro_Z_vs_SMC 3 7.680 1.81e-08 1.402
DEMetro_Z_vs_SMC 4 28.834 6.7e-23 5.264
DEMetro_Z_vs_SMC 5 36.478 8.74e-26 6.660
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.028 0.022 0.012 0.521
HMC 3 0.024 0.019 0.016 0.341
HMC 5 0.046 0.017 0.010 2.904
HMC 8 0.047 0.019 0.014 1.975
HMC 15 0.042 0.019 0.012 1.873
HMC 30 0.097 0.024 0.011 6.666
SMC 2 0.018 0.022 0.012 -0.351
SMC 3 0.018 0.019 0.016 -0.045
SMC 5 0.016 0.017 0.010 -0.072
SMC 8 0.018 0.019 0.014 -0.059
SMC 15 0.020 0.019 0.012 0.044
SMC 30 0.021 0.024 0.011 -0.291
Metro 2 0.147 0.022 0.012 10.408
Metro 3 0.180 0.019 0.016 10.378
Metro 5 0.290 0.017 0.010 27.186
Metro 8 0.364 0.019 0.014 23.958
Metro 15 0.447 0.019 0.012 34.438
Metro 30 0.781 0.024 0.011 68.745
DEMetro_Z 2 0.029 0.022 0.012 0.604
DEMetro_Z 3 0.193 0.019 0.016 11.172
DEMetro_Z 5 6.535 0.017 0.010 648.043
DEMetro_Z 8 7.795 0.019 0.014 540.024
DEMetro_Z 15 9.260 0.019 0.012 743.445
DEMetro_Z 30 11.162 0.024 0.011 1011.243
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 5.216 8.55e-06 3.171
HMC 3 2.565 0.0132 0.790
HMC 5 2.996 0.00479 1.458
HMC 8 3.675 0.000603 1.299
HMC 15 5.770 2.15e-06 4.843
HMC 30 4.283 0.000162 3.885
SMC 2 2.195 0.0329 0.751
SMC 3 -1.106 0.274 -0.294
SMC 5 0.163 0.871 0.044
SMC 8 0.541 0.59 0.136
SMC 15 1.552 0.127 0.522
SMC 30 -1.229 0.224 -0.278
Metro 2 5.670 3.71e-06 10.739
Metro 3 5.477 5.68e-06 6.037
Metro 5 7.901 7.48e-09 9.583
Metro 8 5.950 1.74e-06 13.498
Metro 15 8.690 1.37e-09 30.112
Metro 30 12.453 2.81e-13 24.165
DEMetro_Z 2 4.953 2.06e-05 3.399
DEMetro_Z 3 2.391 0.0235 107.366
DEMetro_Z 5 2.557 0.0161 3644.017
DEMetro_Z 8 4.880 3.54e-05 1617.885
DEMetro_Z 15 12.609 2.7e-13 1860.820
DEMetro_Z 30 14.804 4.71e-15 978.458
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 3.796 0.000694 0.693
HMC_vs_SMC 1 3.540 0.00137 0.646
HMC_vs_SMC 2 3.146 0.00381 0.574
HMC_vs_SMC 3 3.495 0.00154 0.638
HMC_vs_SMC 4 5.070 2.09e-05 0.926
HMC_vs_SMC 5 4.591 7.89e-05 0.838
Metro_vs_DEMetro_Z 0 3.548 0.00134 0.648
Metro_vs_DEMetro_Z 1 -2.244 0.0326 -0.410
Metro_vs_DEMetro_Z 2 -2.550 0.0163 -0.465
Metro_vs_DEMetro_Z 3 -4.845 3.9e-05 -0.885
Metro_vs_DEMetro_Z 4 -12.418 3.93e-13 -2.267
Metro_vs_DEMetro_Z 5 -14.323 1.1e-14 -2.615
HMC_vs_Metro 0 -3.992 0.000409 -0.729
HMC_vs_Metro 1 -5.048 2.22e-05 -0.922
HMC_vs_Metro 2 -6.451 4.66e-07 -1.178
HMC_vs_Metro 3 -5.598 4.82e-06 -1.022
HMC_vs_Metro 4 -6.869 1.52e-07 -1.254
HMC_vs_Metro 5 -11.833 1.27e-12 -2.160
HMC_vs_DEMetro_Z 0 -0.267 0.791 -0.049
HMC_vs_DEMetro_Z 1 -2.375 0.0244 -0.434
HMC_vs_DEMetro_Z 2 -2.555 0.0161 -0.467
HMC_vs_DEMetro_Z 3 -4.877 3.57e-05 -0.890
HMC_vs_DEMetro_Z 4 -12.596 2.77e-13 -2.300
HMC_vs_DEMetro_Z 5 -14.691 5.74e-15 -2.682
Metro_vs_SMC 0 5.303 1.09e-05 0.968
Metro_vs_SMC 1 5.782 2.9e-06 1.056
Metro_vs_SMC 2 7.687 1.78e-08 1.403
Metro_vs_SMC 3 5.839 2.48e-06 1.066
Metro_vs_SMC 4 8.662 1.55e-09 1.581
Metro_vs_SMC 5 12.751 2.04e-13 2.328
DEMetro_Z_vs_SMC 0 3.702 0.000892 0.676
DEMetro_Z_vs_SMC 1 2.397 0.0232 0.438
DEMetro_Z_vs_SMC 2 2.557 0.0161 0.467
DEMetro_Z_vs_SMC 3 4.880 3.54e-05 0.891
DEMetro_Z_vs_SMC 4 12.605 2.72e-13 2.301
DEMetro_Z_vs_SMC 5 14.804 4.71e-15 2.703
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.054 0.019 0.011 3.171
HMC 3 0.045 0.030 0.019 0.790
HMC 5 0.051 0.028 0.015 1.458
HMC 8 0.049 0.026 0.018 1.299
HMC 15 0.086 0.024 0.013 4.843
HMC 30 0.113 0.029 0.022 3.885
SMC 2 0.027 0.019 0.011 0.751
SMC 3 0.025 0.030 0.019 -0.294
SMC 5 0.029 0.028 0.015 0.044
SMC 8 0.028 0.026 0.018 0.136
SMC 15 0.031 0.024 0.013 0.522
SMC 30 0.023 0.029 0.022 -0.278
Metro 2 0.138 0.019 0.011 10.739
Metro 3 0.145 0.030 0.019 6.037
Metro 5 0.174 0.028 0.015 9.583
Metro 8 0.265 0.026 0.018 13.498
Metro 15 0.410 0.024 0.013 30.112
Metro 30 0.549 0.029 0.022 24.165
DEMetro_Z 2 0.057 0.019 0.011 3.399
DEMetro_Z 3 2.071 0.030 0.019 107.366
DEMetro_Z 5 55.533 0.028 0.015 3644.017
DEMetro_Z 8 28.737 0.026 0.018 1617.885
DEMetro_Z 15 23.857 0.024 0.013 1860.820
DEMetro_Z 30 21.092 0.029 0.022 978.458
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 3.863 0.000356 1.460
HMC 3 2.839 0.00625 0.777
HMC 5 6.558 2.07e-07 5.110
HMC 8 5.612 2.26e-06 3.060
HMC 15 7.199 2.5e-08 4.639
HMC 30 8.379 2.17e-09 10.227
SMC 2 -1.082 0.284 -0.266
SMC 3 -1.038 0.304 -0.232
SMC 5 0.313 0.756 0.106
SMC 8 -0.508 0.613 -0.122
SMC 15 1.241 0.22 0.348
SMC 30 -0.915 0.364 -0.267
Metro 2 7.395 3.47e-08 16.005
Metro 3 8.576 1.51e-09 13.136
Metro 5 8.968 7.22e-10 50.841
Metro 8 8.654 1.53e-09 37.230
Metro 15 9.189 4.27e-10 58.870
Metro 30 8.127 5.79e-09 97.540
DEMetro_Z 2 5.298 4.1e-06 2.232
DEMetro_Z 3 4.550 8.75e-05 15.490
DEMetro_Z 5 6.731 2.19e-07 1249.656
DEMetro_Z 8 8.800 1.1e-09 848.501
DEMetro_Z 15 28.232 1.21e-22 1178.440
DEMetro_Z 30 36.681 7.45e-26 1420.617
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 6.288 7.25e-07 1.148
Metro_vs_DEMetro_Z 1 -0.614 0.544 -0.112
Metro_vs_DEMetro_Z 2 -6.476 4.35e-07 -1.182
Metro_vs_DEMetro_Z 3 -8.313 3.66e-09 -1.518
Metro_vs_DEMetro_Z 4 -25.851 1.42e-21 -4.720
Metro_vs_DEMetro_Z 5 -35.525 1.85e-25 -6.486
DEMetro_Z_vs_SMC 0 5.651 4.17e-06 1.032
DEMetro_Z_vs_SMC 1 4.608 7.52e-05 0.841
DEMetro_Z_vs_SMC 2 6.734 2.17e-07 1.229
DEMetro_Z_vs_SMC 3 8.807 1.09e-09 1.608
DEMetro_Z_vs_SMC 4 28.273 1.16e-22 5.162
DEMetro_Z_vs_SMC 5 36.722 7.23e-26 6.704
HMC_vs_DEMetro_Z 0 -1.488 0.147 -0.272
HMC_vs_DEMetro_Z 1 -4.270 0.000192 -0.780
HMC_vs_DEMetro_Z 2 -6.691 2.44e-07 -1.222
HMC_vs_DEMetro_Z 3 -8.767 1.2e-09 -1.601
HMC_vs_DEMetro_Z 4 -28.272 1.16e-22 -5.162
HMC_vs_DEMetro_Z 5 -36.478 8.74e-26 -6.660
HMC_vs_Metro 0 -6.933 1.28e-07 -1.266
HMC_vs_Metro 1 -8.285 3.92e-09 -1.513
HMC_vs_Metro 2 -7.842 1.2e-08 -1.432
HMC_vs_Metro 3 -7.968 8.7e-09 -1.455
HMC_vs_Metro 4 -8.206 4.77e-09 -1.498
HMC_vs_Metro 5 -7.428 3.48e-08 -1.356
HMC_vs_SMC 0 4.943 2.97e-05 0.902
HMC_vs_SMC 1 4.250 0.000202 0.776
HMC_vs_SMC 2 6.417 5.11e-07 1.172
HMC_vs_SMC 3 6.177 9.8e-07 1.128
HMC_vs_SMC 4 6.404 5.29e-07 1.169
HMC_vs_SMC 5 8.478 2.43e-09 1.548
Metro_vs_SMC 0 7.547 2.55e-08 1.378
Metro_vs_SMC 1 8.827 1.03e-09 1.612
Metro_vs_SMC 2 9.004 6.75e-10 1.644
Metro_vs_SMC 3 8.625 1.69e-09 1.575
Metro_vs_SMC 4 9.164 4.6e-10 1.673
Metro_vs_SMC 5 8.154 5.44e-09 1.489
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.039 0.027 0.008 1.460
HMC 3 0.036 0.028 0.011 0.777
HMC 5 0.047 0.023 0.005 5.110
HMC 8 0.051 0.025 0.008 3.060
HMC 15 0.055 0.024 0.007 4.639
HMC 30 0.095 0.028 0.007 10.227
SMC 2 0.025 0.027 0.008 -0.266
SMC 3 0.025 0.028 0.011 -0.232
SMC 5 0.024 0.023 0.005 0.106
SMC 8 0.024 0.025 0.008 -0.122
SMC 15 0.026 0.024 0.007 0.348
SMC 30 0.026 0.028 0.007 -0.267
Metro 2 0.156 0.027 0.008 16.005
Metro 3 0.170 0.028 0.011 13.136
Metro 5 0.260 0.023 0.005 50.841
Metro 8 0.335 0.025 0.008 37.230
Metro 15 0.420 0.024 0.007 58.870
Metro 30 0.670 0.028 0.007 97.540
DEMetro_Z 2 0.045 0.027 0.008 2.232
DEMetro_Z 3 0.196 0.028 0.011 15.490
DEMetro_Z 5 5.850 0.023 0.005 1249.656
DEMetro_Z 8 7.088 0.025 0.008 848.501
DEMetro_Z 15 7.963 0.024 0.007 1178.440
DEMetro_Z 30 9.387 0.028 0.007 1420.617
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 4.214 0.000129 1.750
HMC 3 3.387 0.00129 0.960
HMC 5 5.724 2.06e-06 3.871
HMC 8 5.823 7.6e-07 2.503
HMC 15 7.666 5.04e-09 4.424
HMC 30 8.582 1.06e-09 8.440
SMC 2 -0.830 0.41 -0.217
SMC 3 -0.735 0.466 -0.165
SMC 5 0.317 0.753 0.116
SMC 8 -0.637 0.527 -0.140
SMC 15 1.257 0.214 0.335
SMC 30 -0.087 0.931 -0.027
Metro 2 8.127 5.01e-09 14.907
Metro 3 8.756 8.84e-10 11.567
Metro 5 9.968 6.78e-11 39.470
Metro 8 10.126 4.53e-11 28.900
Metro 15 11.314 3.58e-12 51.993
Metro 30 10.282 3.45e-11 81.420
DEMetro_Z 2 4.335 9.63e-05 1.966
DEMetro_Z 3 9.001 6.09e-11 4.475
DEMetro_Z 5 17.270 8.3e-17 186.648
DEMetro_Z 8 36.542 6.72e-26 133.069
DEMetro_Z 15 98.534 9.79e-39 190.524
DEMetro_Z 30 78.067 1.36e-35 185.762
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 4.534 9.24e-05 0.828
DEMetro_Z_vs_SMC 1 10.975 7.67e-12 2.004
DEMetro_Z_vs_SMC 2 17.282 8.25e-17 3.155
DEMetro_Z_vs_SMC 3 36.937 6.13e-26 6.744
DEMetro_Z_vs_SMC 4 98.570 3.43e-38 17.996
DEMetro_Z_vs_SMC 5 76.700 4.82e-35 14.003
HMC_vs_Metro 0 -7.306 4.78e-08 -1.334
HMC_vs_Metro 1 -8.473 2.46e-09 -1.547
HMC_vs_Metro 2 -8.690 1.44e-09 -1.587
HMC_vs_Metro 3 -9.229 3.95e-10 -1.685
HMC_vs_Metro 4 -9.923 7.87e-11 -1.812
HMC_vs_Metro 5 -9.536 1.92e-10 -1.741
Metro_vs_DEMetro_Z 0 6.847 1.61e-07 1.250
Metro_vs_DEMetro_Z 1 5.140 1.72e-05 0.938
Metro_vs_DEMetro_Z 2 -13.477 5.14e-14 -2.461
Metro_vs_DEMetro_Z 3 -20.260 1.16e-18 -3.699
Metro_vs_DEMetro_Z 4 -26.309 8.69e-22 -4.803
Metro_vs_DEMetro_Z 5 -13.596 4.12e-14 -2.482
HMC_vs_SMC 0 4.793 4.51e-05 0.875
HMC_vs_SMC 1 4.508 9.92e-05 0.823
HMC_vs_SMC 2 5.939 1.88e-06 1.084
HMC_vs_SMC 3 7.370 4.05e-08 1.346
HMC_vs_SMC 4 7.091 8.42e-08 1.295
HMC_vs_SMC 5 8.292 3.85e-09 1.514
Metro_vs_SMC 0 8.257 4.2e-09 1.507
Metro_vs_SMC 1 9.021 6.48e-10 1.647
Metro_vs_SMC 2 10.028 6.19e-11 1.831
Metro_vs_SMC 3 10.046 5.95e-11 1.834
Metro_vs_SMC 4 11.231 4.45e-12 2.050
Metro_vs_SMC 5 10.316 3.25e-11 1.883
HMC_vs_DEMetro_Z 0 -0.379 0.707 -0.069
HMC_vs_DEMetro_Z 1 -6.495 4.14e-07 -1.186
HMC_vs_DEMetro_Z 2 -16.699 2.05e-16 -3.049
HMC_vs_DEMetro_Z 3 -36.771 6.96e-26 -6.713
HMC_vs_DEMetro_Z 4 -99.151 2.89e-38 -18.102
HMC_vs_DEMetro_Z 5 -73.695 1.53e-34 -13.455
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.023 0.014 0.005 1.750
HMC 3 0.022 0.015 0.007 0.960
HMC 5 0.026 0.013 0.003 3.871
HMC 8 0.030 0.014 0.006 2.503
HMC 15 0.035 0.014 0.005 4.424
HMC 30 0.059 0.016 0.005 8.440
SMC 2 0.013 0.014 0.005 -0.217
SMC 3 0.014 0.015 0.007 -0.165
SMC 5 0.013 0.013 0.003 0.116
SMC 8 0.013 0.014 0.006 -0.140
SMC 15 0.015 0.014 0.005 0.335
SMC 30 0.016 0.016 0.005 -0.027
Metro 2 0.087 0.014 0.005 14.907
Metro 3 0.100 0.015 0.007 11.567
Metro 5 0.148 0.013 0.003 39.470
Metro 8 0.200 0.014 0.006 28.900
Metro 15 0.263 0.014 0.005 51.993
Metro 30 0.428 0.016 0.005 81.420
DEMetro_Z 2 0.024 0.014 0.005 1.966
DEMetro_Z 3 0.048 0.015 0.007 4.475
DEMetro_Z 5 0.652 0.013 0.003 186.648
DEMetro_Z 8 0.872 0.014 0.006 133.069
DEMetro_Z 15 0.927 0.014 0.005 190.524
DEMetro_Z 30 0.956 0.016 0.005 185.762
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
Forest & Ridge Plots
Pooled
2 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
8 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
15 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
30 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
8 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
15 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
30 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2
3
5
8
15
30
Chain
2
3
5
8
15
30

Vary_Dimension_with_heavy_Tails (MvStudentT, dimension, 30 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 0.458 0.648 0.135
HMC 3 0.257 0.798 0.070
HMC 5 -1.326 0.191 -0.293
HMC 8 -0.542 0.59 -0.154
HMC 15 0.190 0.85 0.045
HMC 30 2.278 0.0297 2.172
SMC 2 -0.886 0.38 -0.203
SMC 3 1.720 0.0908 0.429
SMC 5 6.877 9.83e-09 2.322
SMC 8 9.083 3.83e-10 11.549
SMC 15 10.284 1.53e-14 2.453
SMC 30 23.248 9.2e-25 10.558
Metro 2 3.132 0.00361 2.184
Metro 3 2.972 0.00549 2.129
Metro 5 3.267 0.00199 0.706
Metro 8 5.129 1.39e-05 4.358
Metro 15 3.833 0.000421 1.623
Metro 30 7.255 4.84e-08 13.064
DEMetro_Z 2 4.667 2.41e-05 1.602
DEMetro_Z 3 3.847 0.000605 31.759
DEMetro_Z 5 6.579 3.29e-07 72.143
DEMetro_Z 8 6.315 6.73e-07 110.351
DEMetro_Z 15 20.842 4.44e-19 64.809
DEMetro_Z 30 19.763 2.26e-18 407.501
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -4.435 0.000121 -0.810
HMC_vs_DEMetro_Z 1 -3.816 0.000657 -0.697
HMC_vs_DEMetro_Z 2 -6.600 3.12e-07 -1.205
HMC_vs_DEMetro_Z 3 -6.336 6.36e-07 -1.157
HMC_vs_DEMetro_Z 4 -21.053 4.07e-19 -3.844
HMC_vs_DEMetro_Z 5 -19.922 1.83e-18 -3.637
Metro_vs_SMC 0 3.511 0.00148 0.641
Metro_vs_SMC 1 2.384 0.0239 0.435
Metro_vs_SMC 2 -5.329 1.02e-05 -0.973
Metro_vs_SMC 3 -4.301 0.000176 -0.785
Metro_vs_SMC 4 -1.990 0.0561 -0.363
Metro_vs_SMC 5 1.474 0.151 0.269
Metro_vs_DEMetro_Z 0 0.825 0.416 0.151
Metro_vs_DEMetro_Z 1 -3.546 0.00135 -0.647
Metro_vs_DEMetro_Z 2 -6.531 3.75e-07 -1.192
Metro_vs_DEMetro_Z 3 -6.060 1.35e-06 -1.106
Metro_vs_DEMetro_Z 4 -20.038 1.56e-18 -3.658
Metro_vs_DEMetro_Z 5 -19.157 5.26e-18 -3.498
HMC_vs_Metro 0 -2.899 0.00707 -0.529
HMC_vs_Metro 1 -2.963 0.00602 -0.541
HMC_vs_Metro 2 -6.852 1.59e-07 -1.251
HMC_vs_Metro 3 -5.098 1.93e-05 -0.931
HMC_vs_Metro 4 -3.627 0.00109 -0.662
HMC_vs_Metro 5 -5.395 8.46e-06 -0.985
HMC_vs_SMC 0 1.261 0.217 0.230
HMC_vs_SMC 1 -1.248 0.222 -0.228
HMC_vs_SMC 2 -8.027 7.48e-09 -1.466
HMC_vs_SMC 3 -9.030 6.33e-10 -1.649
HMC_vs_SMC 4 -11.417 3.01e-12 -2.084
HMC_vs_SMC 5 -8.192 4.94e-09 -1.496
DEMetro_Z_vs_SMC 0 5.623 4.51e-06 1.027
DEMetro_Z_vs_SMC 1 3.808 0.000671 0.695
DEMetro_Z_vs_SMC 2 6.375 5.73e-07 1.164
DEMetro_Z_vs_SMC 3 5.595 4.86e-06 1.022
DEMetro_Z_vs_SMC 4 19.967 1.72e-18 3.646
DEMetro_Z_vs_SMC 5 19.230 4.74e-18 3.511
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.070 0.065 0.042 0.135
HMC 3 0.069 0.067 0.033 0.070
HMC 5 0.059 0.071 0.043 -0.293
HMC 8 0.057 0.060 0.018 -0.154
HMC 15 0.078 0.076 0.059 0.045
HMC 30 0.095 0.067 0.013 2.172
SMC 2 0.056 0.065 0.042 -0.203
SMC 3 0.081 0.067 0.033 0.429
SMC 5 0.172 0.071 0.043 2.322
SMC 8 0.262 0.060 0.018 11.549
SMC 15 0.221 0.076 0.059 2.453
SMC 30 0.204 0.067 0.013 10.558
Metro 2 0.156 0.065 0.042 2.184
Metro 3 0.137 0.067 0.033 2.129
Metro 5 0.102 0.071 0.043 0.706
Metro 8 0.136 0.060 0.018 4.358
Metro 15 0.172 0.076 0.059 1.623
Metro 30 0.237 0.067 0.013 13.064
DEMetro_Z 2 0.132 0.065 0.042 1.602
DEMetro_Z 3 1.114 0.067 0.033 31.759
DEMetro_Z 5 3.192 0.071 0.043 72.143
DEMetro_Z 8 1.991 0.060 0.018 110.351
DEMetro_Z 15 3.926 0.076 0.059 64.809
DEMetro_Z 30 5.369 0.067 0.013 407.501
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 0.083 0.934 0.031
HMC 3 1.779 0.0833 0.879
HMC 5 -1.584 0.123 -0.297
HMC 8 -0.898 0.374 -0.185
HMC 15 -1.152 0.259 -0.210
HMC 30 1.238 0.225 1.304
SMC 2 -2.065 0.0468 -0.391
SMC 3 1.604 0.117 0.757
SMC 5 -0.763 0.451 -0.140
SMC 8 15.252 5.87e-22 3.920
SMC 15 1.533 0.136 0.281
SMC 30 48.527 1.72e-42 16.968
Metro 2 -0.742 0.462 -0.155
Metro 3 1.583 0.122 0.797
Metro 5 -1.937 0.0625 -0.354
Metro 8 0.357 0.722 0.090
Metro 15 -0.772 0.446 -0.145
Metro 30 2.491 0.0185 3.746
DEMetro_Z 2 -1.657 0.107 -0.315
DEMetro_Z 3 1.954 0.0605 68.481
DEMetro_Z 5 4.194 0.000233 13.108
DEMetro_Z 8 4.484 0.000106 19.988
DEMetro_Z 15 10.355 2.21e-14 3.176
DEMetro_Z 30 15.218 2.18e-15 70.078
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 1.268 0.215 0.231
HMC_vs_SMC 1 0.428 0.672 0.078
HMC_vs_SMC 2 -3.487 0.00158 -0.637
HMC_vs_SMC 3 -21.466 2.39e-19 -3.919
HMC_vs_SMC 4 -36.616 7.85e-26 -6.685
HMC_vs_SMC 5 -18.867 7.92e-18 -3.445
Metro_vs_DEMetro_Z 0 1.611 0.118 0.294
Metro_vs_DEMetro_Z 1 -1.928 0.0637 -0.352
Metro_vs_DEMetro_Z 2 -4.312 0.00017 -0.787
Metro_vs_DEMetro_Z 3 -4.435 0.000122 -0.810
Metro_vs_DEMetro_Z 4 -12.720 2.17e-13 -2.322
Metro_vs_DEMetro_Z 5 -14.510 7.89e-15 -2.649
HMC_vs_Metro 0 0.531 0.6 0.097
HMC_vs_Metro 1 0.312 0.757 0.057
HMC_vs_Metro 2 1.365 0.183 0.249
HMC_vs_Metro 3 -1.750 0.0907 -0.320
HMC_vs_Metro 4 -1.410 0.169 -0.258
HMC_vs_Metro 5 -2.024 0.0523 -0.370
HMC_vs_DEMetro_Z 0 1.034 0.31 0.189
HMC_vs_DEMetro_Z 1 -1.925 0.0641 -0.351
HMC_vs_DEMetro_Z 2 -4.286 0.000183 -0.783
HMC_vs_DEMetro_Z 3 -4.512 9.84e-05 -0.824
HMC_vs_DEMetro_Z 4 -13.718 3.29e-14 -2.504
HMC_vs_DEMetro_Z 5 -15.517 1.4e-15 -2.833
Metro_vs_SMC 0 2.350 0.0258 0.429
Metro_vs_SMC 1 0.110 0.913 0.020
Metro_vs_SMC 2 -9.735 1.21e-10 -1.777
Metro_vs_SMC 3 -15.360 1.82e-15 -2.804
Metro_vs_SMC 4 -8.747 1.26e-09 -1.597
Metro_vs_SMC 5 -9.577 1.74e-10 -1.749
DEMetro_Z_vs_SMC 0 2.304 0.0286 0.421
DEMetro_Z_vs_SMC 1 1.929 0.0636 0.352
DEMetro_Z_vs_SMC 2 4.244 0.000206 0.775
DEMetro_Z_vs_SMC 3 3.615 0.00112 0.660
DEMetro_Z_vs_SMC 4 11.902 1.11e-12 2.173
DEMetro_Z_vs_SMC 5 11.624 1.95e-12 2.122
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 9.559 9.112 14.240 0.031
HMC 3 6.978 4.160 3.204 0.879
HMC 5 6.017 17.558 38.901 -0.297
HMC 8 3.904 5.290 7.509 -0.185
HMC 15 4.516 33.738 138.861 -0.210
HMC 30 12.709 5.218 5.743 1.304
SMC 2 3.545 9.112 14.240 -0.391
SMC 3 6.586 4.160 3.204 0.757
SMC 5 12.110 17.558 38.901 -0.140
SMC 8 34.726 5.290 7.509 3.920
SMC 15 72.691 33.738 138.861 0.281
SMC 30 102.675 5.218 5.743 16.968
Metro 2 6.906 9.112 14.240 -0.155
Metro 3 6.714 4.160 3.204 0.797
Metro 5 3.775 17.558 38.901 -0.354
Metro 8 5.968 5.290 7.509 0.090
Metro 15 13.581 33.738 138.861 -0.145
Metro 30 26.734 5.218 5.743 3.746
DEMetro_Z 2 4.632 9.112 14.240 -0.315
DEMetro_Z 3 223.595 4.160 3.204 68.481
DEMetro_Z 5 527.482 17.558 38.901 13.108
DEMetro_Z 8 155.377 5.290 7.509 19.988
DEMetro_Z 15 474.759 33.738 138.861 3.176
DEMetro_Z 30 407.712 5.218 5.743 70.078
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 2.468 0.0183 1.261
HMC 3 4.560 5.17e-05 2.230
HMC 5 2.262 0.0299 1.288
HMC 8 3.466 0.0014 1.987
HMC 15 3.162 0.00286 1.258
HMC 30 4.800 4.32e-05 11.925
SMC 2 -0.073 0.942 -0.017
SMC 3 7.045 7.18e-08 8.145
SMC 5 22.328 2.62e-20 29.214
SMC 8 35.919 1.12e-25 137.443
SMC 15 68.811 1.35e-34 95.580
SMC 30 156.745 1.79e-44 364.345
Metro 2 4.852 2.93e-05 3.644
Metro 3 5.598 4.29e-06 7.678
Metro 5 6.731 1.6e-08 2.250
Metro 8 4.607 7.21e-05 7.742
Metro 15 3.655 0.000991 6.722
Metro 30 5.691 3.73e-06 55.865
DEMetro_Z 2 8.865 4.66e-11 3.868
DEMetro_Z 3 5.079 2.04e-05 153.234
DEMetro_Z 5 8.395 2.98e-09 201.625
DEMetro_Z 8 9.086 5.54e-10 241.537
DEMetro_Z 15 29.058 5.23e-23 260.038
DEMetro_Z 30 33.931 6.77e-25 742.551
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -0.247 0.807 -0.045
Metro_vs_DEMetro_Z 1 -4.813 4.27e-05 -0.879
Metro_vs_DEMetro_Z 2 -8.309 3.69e-09 -1.517
Metro_vs_DEMetro_Z 3 -8.676 1.49e-09 -1.584
Metro_vs_DEMetro_Z 4 -27.551 2.4e-22 -5.030
Metro_vs_DEMetro_Z 5 -30.035 2.13e-23 -5.484
DEMetro_Z_vs_SMC 0 9.223 4e-10 1.684
DEMetro_Z_vs_SMC 1 4.769 4.82e-05 0.871
DEMetro_Z_vs_SMC 2 7.109 8.02e-08 1.298
DEMetro_Z_vs_SMC 3 3.923 0.000492 0.716
DEMetro_Z_vs_SMC 4 19.016 6.42e-18 3.472
DEMetro_Z_vs_SMC 5 17.371 7.21e-17 3.171
HMC_vs_DEMetro_Z 0 -4.134 0.000277 -0.755
HMC_vs_DEMetro_Z 1 -5.002 2.53e-05 -0.913
HMC_vs_DEMetro_Z 2 -8.321 3.58e-09 -1.519
HMC_vs_DEMetro_Z 3 -9.031 6.33e-10 -1.649
HMC_vs_DEMetro_Z 4 -29.019 5.6e-23 -5.298
HMC_vs_DEMetro_Z 5 -32.977 1.52e-24 -6.021
HMC_vs_Metro 0 -2.680 0.012 -0.489
HMC_vs_Metro 1 -4.292 0.00018 -0.784
HMC_vs_Metro 2 -1.635 0.113 -0.298
HMC_vs_Metro 3 -3.161 0.00367 -0.577
HMC_vs_Metro 4 -2.849 0.00798 -0.520
HMC_vs_Metro 5 -4.253 0.000201 -0.776
HMC_vs_SMC 0 2.541 0.0167 0.464
HMC_vs_SMC 1 -4.635 7e-05 -0.846
HMC_vs_SMC 2 -21.375 2.69e-19 -3.903
HMC_vs_SMC 3 -34.677 3.68e-25 -6.331
HMC_vs_SMC 4 -63.978 8.99e-33 -11.681
HMC_vs_SMC 5 -102.768 1.03e-38 -18.763
Metro_vs_SMC 0 4.742 5.19e-05 0.866
Metro_vs_SMC 1 -0.262 0.795 -0.048
Metro_vs_SMC 2 -20.552 7.84e-19 -3.752
Metro_vs_SMC 3 -32.468 2.37e-24 -5.928
Metro_vs_SMC 4 -41.885 1.71e-27 -7.647
Metro_vs_SMC 5 -31.634 4.94e-24 -5.775
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.168 0.124 0.035 1.261
HMC 3 0.154 0.115 0.018 2.230
HMC 5 0.176 0.126 0.039 1.288
HMC 8 0.155 0.113 0.021 1.987
HMC 15 0.204 0.136 0.054 1.258
HMC 30 0.338 0.118 0.018 11.925
SMC 2 0.123 0.124 0.035 -0.017
SMC 3 0.258 0.115 0.018 8.145
SMC 5 1.264 0.126 0.039 29.214
SMC 8 3.008 0.113 0.021 137.443
SMC 15 5.321 0.136 0.054 95.580
SMC 30 6.844 0.118 0.018 364.345
Metro 2 0.251 0.124 0.035 3.644
Metro 3 0.250 0.115 0.018 7.678
Metro 5 0.214 0.126 0.039 2.250
Metro 8 0.276 0.113 0.021 7.742
Metro 15 0.500 0.136 0.054 6.722
Metro 30 1.149 0.118 0.018 55.865
DEMetro_Z 2 0.259 0.124 0.035 3.868
DEMetro_Z 3 2.804 0.115 0.018 153.234
DEMetro_Z 5 7.982 0.126 0.039 201.625
DEMetro_Z 8 5.200 0.113 0.021 241.537
DEMetro_Z 15 14.243 0.136 0.054 260.038
DEMetro_Z 30 13.826 0.118 0.018 742.551
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 3.862 0.000298 1.131
HMC 3 2.399 0.0222 1.654
HMC 5 3.158 0.00359 3.974
HMC 8 3.444 0.00171 4.789
HMC 15 4.317 0.000166 12.414
HMC 30 5.178 1.53e-05 23.104
SMC 2 2.537 0.0144 0.870
SMC 3 8.189 3.77e-09 11.045
SMC 5 35.088 1.84e-25 97.363
SMC 8 69.912 2.99e-34 152.941
SMC 15 144.383 2.92e-44 197.963
SMC 30 152.964 1.75e-45 180.136
Metro 2 7.089 2.38e-08 3.835
Metro 3 8.539 7.04e-10 6.047
Metro 5 8.966 5.3e-10 12.011
Metro 8 6.798 1.68e-07 13.840
Metro 15 6.590 3.16e-07 34.086
Metro 30 10.173 4.4e-11 73.055
DEMetro_Z 2 9.219 1.21e-10 6.660
DEMetro_Z 3 10.521 2e-11 54.324
DEMetro_Z 5 27.993 1.45e-22 175.522
DEMetro_Z 8 28.865 6.07e-23 171.304
DEMetro_Z 15 83.035 2.8e-36 233.126
DEMetro_Z 30 79.217 1.11e-35 223.737
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 6.807 1.79e-07 1.243
DEMetro_Z_vs_SMC 1 7.983 8.36e-09 1.458
DEMetro_Z_vs_SMC 2 11.060 6.39e-12 2.019
DEMetro_Z_vs_SMC 3 2.819 0.00859 0.515
DEMetro_Z_vs_SMC 4 12.271 5.25e-13 2.240
DEMetro_Z_vs_SMC 5 12.659 2.45e-13 2.311
HMC_vs_Metro 0 -4.851 3.84e-05 -0.886
HMC_vs_Metro 1 -4.468 0.000111 -0.816
HMC_vs_Metro 2 -4.454 0.000115 -0.813
HMC_vs_Metro 3 -3.602 0.00116 -0.658
HMC_vs_Metro 4 -3.531 0.0014 -0.645
HMC_vs_Metro 5 -5.872 2.27e-06 -1.072
Metro_vs_DEMetro_Z 0 -3.739 0.000809 -0.683
Metro_vs_DEMetro_Z 1 -9.426 2.48e-10 -1.721
Metro_vs_DEMetro_Z 2 -26.137 1.04e-21 -4.772
Metro_vs_DEMetro_Z 3 -24.340 7.54e-21 -4.444
Metro_vs_DEMetro_Z 4 -42.403 1.2e-27 -7.742
Metro_vs_DEMetro_Z 5 -19.817 2.11e-18 -3.618
HMC_vs_SMC 0 0.703 0.488 0.128
HMC_vs_SMC 1 -6.137 1.09e-06 -1.120
HMC_vs_SMC 2 -33.745 7.95e-25 -6.161
HMC_vs_SMC 3 -53.724 1.37e-30 -9.809
HMC_vs_SMC 4 -57.657 1.79e-31 -10.527
HMC_vs_SMC 5 -37.732 3.34e-26 -6.889
Metro_vs_SMC 0 4.754 5.03e-05 0.868
Metro_vs_SMC 1 -3.344 0.00229 -0.611
Metro_vs_SMC 2 -27.846 1.78e-22 -5.084
Metro_vs_SMC 3 -50.972 6.19e-30 -9.306
Metro_vs_SMC 4 -32.794 1.78e-24 -5.987
Metro_vs_SMC 5 -15.186 2.44e-15 -2.773
HMC_vs_DEMetro_Z 0 -7.235 5.76e-08 -1.321
HMC_vs_DEMetro_Z 1 -10.185 4.35e-11 -1.860
HMC_vs_DEMetro_Z 2 -26.879 4.78e-22 -4.907
HMC_vs_DEMetro_Z 3 -28.417 1.01e-22 -5.188
HMC_vs_DEMetro_Z 4 -56.422 3.35e-31 -10.301
HMC_vs_DEMetro_Z 5 -34.094 5.94e-25 -6.225
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.020 0.015 0.005 1.131
HMC 3 0.021 0.015 0.003 1.654
HMC 5 0.023 0.014 0.002 3.974
HMC 8 0.026 0.015 0.002 4.789
HMC 15 0.040 0.015 0.002 12.414
HMC 30 0.064 0.016 0.002 23.104
SMC 2 0.019 0.015 0.005 0.870
SMC 3 0.053 0.015 0.003 11.045
SMC 5 0.230 0.014 0.002 97.363
SMC 8 0.361 0.015 0.002 152.941
SMC 15 0.415 0.015 0.002 197.963
SMC 30 0.393 0.016 0.002 180.136
Metro 2 0.032 0.015 0.005 3.835
Metro 3 0.036 0.015 0.003 6.047
Metro 5 0.041 0.014 0.002 12.011
Metro 8 0.046 0.015 0.002 13.840
Metro 15 0.084 0.015 0.002 34.086
Metro 30 0.169 0.016 0.002 73.055
DEMetro_Z 2 0.045 0.015 0.005 6.660
DEMetro_Z 3 0.203 0.015 0.003 54.324
DEMetro_Z 5 0.403 0.014 0.002 175.522
DEMetro_Z 8 0.402 0.015 0.002 171.304
DEMetro_Z 15 0.486 0.015 0.002 233.126
DEMetro_Z 30 0.485 0.016 0.002 223.737
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 1.003 0.32 0.290
HMC 3 -1.210 0.231 -0.281
HMC 5 -1.247 0.219 -0.253
HMC 8 0.871 0.39 0.466
HMC 15 1.542 0.133 1.401
HMC 30 1.805 0.0814 9.437
SMC 2 -1.225 0.226 -0.303
SMC 3 1.905 0.0632 0.718
SMC 5 7.794 3.29e-09 4.413
SMC 8 11.448 2.02e-12 18.688
SMC 15 10.569 5.76e-13 5.037
SMC 30 17.995 2.48e-18 14.569
Metro 2 2.556 0.0155 2.083
Metro 3 2.671 0.0117 2.006
Metro 5 2.214 0.0329 1.092
Metro 8 2.463 0.0199 6.283
Metro 15 1.186 0.245 8.991
Metro 30 6.278 5.57e-07 6.254
DEMetro_Z 2 4.275 0.000129 2.214
DEMetro_Z 3 3.411 0.00192 12.888
DEMetro_Z 5 4.406 0.000131 29.093
DEMetro_Z 8 6.741 2.12e-07 50.666
DEMetro_Z 15 12.661 2.33e-13 60.080
DEMetro_Z 30 24.417 6.85e-21 381.329
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -3.842 0.000614 -0.701
HMC_vs_DEMetro_Z 1 -3.505 0.00151 -0.640
HMC_vs_DEMetro_Z 2 -4.447 0.000118 -0.812
HMC_vs_DEMetro_Z 3 -6.593 3.17e-07 -1.204
HMC_vs_DEMetro_Z 4 -12.306 4.9e-13 -2.247
HMC_vs_DEMetro_Z 5 -22.023 1.19e-19 -4.021
Metro_vs_SMC 0 2.955 0.00614 0.540
Metro_vs_SMC 1 1.501 0.144 0.274
Metro_vs_SMC 2 -4.500 0.000102 -0.822
Metro_vs_SMC 3 -4.034 0.000365 -0.736
Metro_vs_SMC 4 0.514 0.611 0.094
Metro_vs_SMC 5 -6.638 2.81e-07 -1.212
Metro_vs_DEMetro_Z 0 -0.129 0.898 -0.024
Metro_vs_DEMetro_Z 1 -2.745 0.0103 -0.501
Metro_vs_DEMetro_Z 2 -4.214 0.000223 -0.769
Metro_vs_DEMetro_Z 3 -5.560 5.36e-06 -1.015
Metro_vs_DEMetro_Z 4 -5.740 3.26e-06 -1.048
Metro_vs_DEMetro_Z 5 -23.988 1.13e-20 -4.380
HMC_vs_Metro 0 -2.186 0.0371 -0.399
HMC_vs_Metro 1 -3.177 0.00352 -0.580
HMC_vs_Metro 2 -2.859 0.00779 -0.522
HMC_vs_Metro 3 -2.202 0.0358 -0.402
HMC_vs_Metro 4 -0.989 0.331 -0.181
HMC_vs_Metro 5 0.644 0.525 0.118
HMC_vs_SMC 0 2.589 0.0149 0.473
HMC_vs_SMC 1 -2.572 0.0155 -0.470
HMC_vs_SMC 2 -8.548 2.04e-09 -1.561
HMC_vs_SMC 3 -11.821 1.3e-12 -2.158
HMC_vs_SMC 4 -3.998 0.000402 -0.730
HMC_vs_SMC 5 -0.976 0.337 -0.178
DEMetro_Z_vs_SMC 0 5.050 2.2e-05 0.922
DEMetro_Z_vs_SMC 1 3.193 0.00338 0.583
DEMetro_Z_vs_SMC 2 3.767 0.000749 0.688
DEMetro_Z_vs_SMC 3 4.103 0.000302 0.749
DEMetro_Z_vs_SMC 4 11.572 2.18e-12 2.113
DEMetro_Z_vs_SMC 5 23.338 2.41e-20 4.261
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.077 0.065 0.042 0.290
HMC 3 0.058 0.067 0.033 -0.281
HMC 5 0.061 0.071 0.043 -0.253
HMC 8 0.068 0.060 0.018 0.466
HMC 15 0.159 0.076 0.059 1.401
HMC 30 0.189 0.067 0.013 9.437
SMC 2 0.052 0.065 0.042 -0.303
SMC 3 0.091 0.067 0.033 0.718
SMC 5 0.262 0.071 0.043 4.413
SMC 8 0.387 0.060 0.018 18.688
SMC 15 0.375 0.076 0.059 5.037
SMC 30 0.256 0.067 0.013 14.569
Metro 2 0.152 0.065 0.042 2.083
Metro 3 0.133 0.067 0.033 2.006
Metro 5 0.119 0.071 0.043 1.092
Metro 8 0.170 0.060 0.018 6.283
Metro 15 0.610 0.076 0.059 8.991
Metro 30 0.148 0.067 0.013 6.254
DEMetro_Z 2 0.158 0.065 0.042 2.214
DEMetro_Z 3 0.492 0.067 0.033 12.888
DEMetro_Z 5 1.330 0.071 0.043 29.093
DEMetro_Z 8 0.947 0.060 0.018 50.666
DEMetro_Z 15 3.645 0.076 0.059 60.080
DEMetro_Z 30 5.029 0.067 0.013 381.329
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 0.555 0.582 0.255
HMC 3 1.228 0.227 0.624
HMC 5 -1.843 0.0752 -0.340
HMC 8 -0.674 0.504 -0.142
HMC 15 -0.672 0.506 -0.131
HMC 30 1.006 0.322 1.067
SMC 2 -2.223 0.0333 -0.417
SMC 3 1.050 0.302 0.855
SMC 5 -0.994 0.327 -0.187
SMC 8 8.941 6.42e-12 3.005
SMC 15 1.065 0.295 0.196
SMC 30 47.861 1.37e-40 17.896
Metro 2 -0.394 0.695 -0.090
Metro 3 1.848 0.0725 0.936
Metro 5 -1.674 0.104 -0.310
Metro 8 0.671 0.506 0.267
Metro 15 0.676 0.504 0.418
Metro 30 1.594 0.121 1.733
DEMetro_Z 2 -0.983 0.331 -0.196
DEMetro_Z 3 1.624 0.115 8.572
DEMetro_Z 5 2.092 0.0452 4.185
DEMetro_Z 8 2.961 0.00582 2.905
DEMetro_Z 15 5.306 2.94e-06 1.895
DEMetro_Z 30 9.212 3.86e-10 29.666
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 1.575 0.126 0.288
HMC_vs_SMC 1 -0.302 0.765 -0.055
HMC_vs_SMC 2 -2.724 0.0108 -0.497
HMC_vs_SMC 3 -9.993 6.7e-11 -1.825
HMC_vs_SMC 4 -4.269 0.000192 -0.779
HMC_vs_SMC 5 -18.870 7.9e-18 -3.445
Metro_vs_DEMetro_Z 0 0.715 0.48 0.131
Metro_vs_DEMetro_Z 1 -1.430 0.163 -0.261
Metro_vs_DEMetro_Z 2 -2.251 0.0321 -0.411
Metro_vs_DEMetro_Z 3 -2.556 0.0161 -0.467
Metro_vs_DEMetro_Z 4 -2.241 0.0328 -0.409
Metro_vs_DEMetro_Z 5 -8.052 7.03e-09 -1.470
HMC_vs_Metro 0 0.786 0.438 0.144
HMC_vs_Metro 1 -0.819 0.419 -0.150
HMC_vs_Metro 2 -0.718 0.478 -0.131
HMC_vs_Metro 3 -1.147 0.261 -0.209
HMC_vs_Metro 4 -0.919 0.366 -0.168
HMC_vs_Metro 5 -2.030 0.0516 -0.371
HMC_vs_DEMetro_Z 0 1.029 0.312 0.188
HMC_vs_DEMetro_Z 1 -1.491 0.147 -0.272
HMC_vs_DEMetro_Z 2 -2.276 0.0304 -0.416
HMC_vs_DEMetro_Z 3 -3.183 0.00346 -0.581
HMC_vs_DEMetro_Z 4 -6.419 5.08e-07 -1.172
HMC_vs_DEMetro_Z 5 -8.379 3.1e-09 -1.530
Metro_vs_SMC 0 2.456 0.0203 0.448
Metro_vs_SMC 1 0.103 0.918 0.019
Metro_vs_SMC 2 -2.212 0.035 -0.404
Metro_vs_SMC 3 -5.234 1.32e-05 -0.956
Metro_vs_SMC 4 0.370 0.714 0.068
Metro_vs_SMC 5 -16.859 1.59e-16 -3.078
DEMetro_Z_vs_SMC 0 3.528 0.00141 0.644
DEMetro_Z_vs_SMC 1 1.435 0.162 0.262
DEMetro_Z_vs_SMC 2 2.192 0.0366 0.400
DEMetro_Z_vs_SMC 3 -0.099 0.922 -0.018
DEMetro_Z_vs_SMC 4 5.432 7.65e-06 0.992
DEMetro_Z_vs_SMC 5 3.743 0.0008 0.683
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 12.744 9.112 14.240 0.255
HMC 3 6.161 4.160 3.204 0.624
HMC 5 4.329 17.558 38.901 -0.340
HMC 8 4.226 5.290 7.509 -0.142
HMC 15 15.506 33.738 138.861 -0.131
HMC 30 11.344 5.218 5.743 1.067
SMC 2 3.173 9.112 14.240 -0.417
SMC 3 6.901 4.160 3.204 0.855
SMC 5 10.297 17.558 38.901 -0.187
SMC 8 27.856 5.290 7.509 3.005
SMC 15 60.985 33.738 138.861 0.196
SMC 30 108.004 5.218 5.743 17.896
Metro 2 7.833 9.112 14.240 -0.090
Metro 3 7.158 4.160 3.204 0.936
Metro 5 5.494 17.558 38.901 -0.310
Metro 8 7.293 5.290 7.509 0.267
Metro 15 91.748 33.738 138.861 0.418
Metro 30 15.170 5.218 5.743 1.733
DEMetro_Z 2 6.319 9.112 14.240 -0.196
DEMetro_Z 3 31.627 4.160 3.204 8.572
DEMetro_Z 5 180.374 17.558 38.901 4.185
DEMetro_Z 8 27.102 5.290 7.509 2.905
DEMetro_Z 15 296.877 33.738 138.861 1.895
DEMetro_Z 30 175.604 5.218 5.743 29.666
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 2.412 0.0214 1.565
HMC 3 3.038 0.00448 1.798
HMC 5 1.390 0.17 0.360
HMC 8 3.794 0.000584 2.481
HMC 15 2.792 0.00911 5.616
HMC 30 3.487 0.00157 16.864
SMC 2 -0.728 0.47 -0.179
SMC 3 4.804 4.01e-05 6.309
SMC 5 13.634 2.6e-14 23.198
SMC 8 19.998 1.56e-18 113.357
SMC 15 29.271 3.27e-23 83.791
SMC 30 123.490 2.84e-41 369.493
Metro 2 3.675 0.000901 3.894
Metro 3 6.543 2.65e-07 6.545
Metro 5 6.238 2.65e-07 3.055
Metro 8 3.681 0.000932 8.986
Metro 15 1.518 0.14 18.655
Metro 30 4.794 4.47e-05 22.312
DEMetro_Z 2 6.184 5.52e-07 4.365
DEMetro_Z 3 3.550 0.00134 44.381
DEMetro_Z 5 4.027 0.000372 73.721
DEMetro_Z 8 6.683 2.49e-07 94.597
DEMetro_Z 15 12.959 1.36e-13 196.007
DEMetro_Z 30 19.411 3.67e-18 485.364
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -0.362 0.72 -0.066
Metro_vs_DEMetro_Z 1 -2.961 0.00606 -0.541
Metro_vs_DEMetro_Z 2 -3.846 0.000607 -0.702
Metro_vs_DEMetro_Z 3 -5.994 1.62e-06 -1.094
Metro_vs_DEMetro_Z 4 -9.203 4.2e-10 -1.680
Metro_vs_DEMetro_Z 5 -18.388 1.58e-17 -3.357
DEMetro_Z_vs_SMC 0 6.635 2.83e-07 1.211
DEMetro_Z_vs_SMC 1 2.989 0.00566 0.546
DEMetro_Z_vs_SMC 2 2.743 0.0103 0.501
DEMetro_Z_vs_SMC 3 -1.300 0.204 -0.237
DEMetro_Z_vs_SMC 4 6.882 1.46e-07 1.257
DEMetro_Z_vs_SMC 5 4.743 5.18e-05 0.866
HMC_vs_DEMetro_Z 0 -3.348 0.00227 -0.611
HMC_vs_DEMetro_Z 1 -3.368 0.00215 -0.615
HMC_vs_DEMetro_Z 2 -4.005 0.000395 -0.731
HMC_vs_DEMetro_Z 3 -6.465 4.48e-07 -1.180
HMC_vs_DEMetro_Z 4 -12.346 4.53e-13 -2.254
HMC_vs_DEMetro_Z 5 -18.106 2.39e-17 -3.306
HMC_vs_Metro 0 -1.967 0.0588 -0.359
HMC_vs_Metro 1 -4.799 4.43e-05 -0.876
HMC_vs_Metro 2 -5.201 1.45e-05 -0.950
HMC_vs_Metro 3 -2.504 0.0182 -0.457
HMC_vs_Metro 4 -1.033 0.31 -0.189
HMC_vs_Metro 5 -0.862 0.396 -0.157
HMC_vs_SMC 0 2.813 0.00871 0.514
HMC_vs_SMC 1 -3.088 0.00441 -0.564
HMC_vs_SMC 2 -12.788 1.9e-13 -2.335
HMC_vs_SMC 3 -19.765 2.26e-18 -3.609
HMC_vs_SMC 4 -24.259 8.27e-21 -4.429
HMC_vs_SMC 5 -60.676 4.14e-32 -11.078
Metro_vs_SMC 0 3.889 0.000541 0.710
Metro_vs_SMC 1 0.144 0.887 0.026
Metro_vs_SMC 2 -11.213 4.62e-12 -2.047
Metro_vs_SMC 3 -15.527 1.37e-15 -2.835
Metro_vs_SMC 4 -4.862 3.72e-05 -0.888
Metro_vs_SMC 5 -60.744 4e-32 -11.090
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.179 0.124 0.035 1.565
HMC 3 0.146 0.115 0.018 1.798
HMC 5 0.140 0.126 0.039 0.360
HMC 8 0.166 0.113 0.021 2.481
HMC 15 0.440 0.136 0.054 5.616
HMC 30 0.429 0.118 0.018 16.864
SMC 2 0.118 0.124 0.035 -0.179
SMC 3 0.225 0.115 0.018 6.309
SMC 5 1.030 0.126 0.039 23.198
SMC 8 2.500 0.113 0.021 113.357
SMC 15 4.681 0.136 0.054 83.791
SMC 30 6.939 0.118 0.018 369.493
Metro 2 0.260 0.124 0.035 3.894
Metro 3 0.230 0.115 0.018 6.545
Metro 5 0.245 0.126 0.039 3.055
Metro 8 0.303 0.113 0.021 8.986
Metro 15 1.148 0.136 0.054 18.655
Metro 30 0.530 0.118 0.018 22.312
DEMetro_Z 2 0.276 0.124 0.035 4.365
DEMetro_Z 3 0.894 0.115 0.018 44.381
DEMetro_Z 5 2.998 0.126 0.039 73.721
DEMetro_Z 8 2.105 0.113 0.021 94.597
DEMetro_Z 15 10.769 0.136 0.054 196.007
DEMetro_Z 30 9.078 0.118 0.018 485.364
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 2.890 0.0059 1.089
HMC 3 3.448 0.00128 1.404
HMC 5 4.360 9.82e-05 2.218
HMC 8 2.632 0.0134 5.533
HMC 15 2.581 0.0152 34.188
HMC 30 2.754 0.01 47.294
SMC 2 0.849 0.4 0.221
SMC 3 7.061 7.26e-08 9.064
SMC 5 23.412 1.92e-20 88.696
SMC 8 31.555 4.66e-24 140.193
SMC 15 75.900 3.34e-35 190.517
SMC 30 148.111 7.8e-45 186.557
Metro 2 8.118 1.16e-09 4.454
Metro 3 8.550 6.18e-10 5.796
Metro 5 10.958 4.39e-12 12.970
Metro 8 8.608 1.34e-09 12.191
Metro 15 8.169 5.13e-09 40.552
Metro 30 8.830 9.95e-10 38.157
DEMetro_Z 2 9.015 4.19e-11 4.190
DEMetro_Z 3 6.327 6.37e-07 21.848
DEMetro_Z 5 8.741 1.27e-09 96.839
DEMetro_Z 8 15.140 2.6e-15 132.368
DEMetro_Z 15 35.345 2.02e-25 242.889
DEMetro_Z 30 65.404 3.64e-33 248.741
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 8.643 1.62e-09 1.578
DEMetro_Z_vs_SMC 1 3.215 0.00319 0.587
DEMetro_Z_vs_SMC 2 0.695 0.493 0.127
DEMetro_Z_vs_SMC 3 -0.856 0.399 -0.156
DEMetro_Z_vs_SMC 4 7.363 4.12e-08 1.344
DEMetro_Z_vs_SMC 5 14.552 7.33e-15 2.657
HMC_vs_Metro 0 -5.628 4.44e-06 -1.028
HMC_vs_Metro 1 -6.324 6.57e-07 -1.155
HMC_vs_Metro 2 -8.092 6.36e-09 -1.477
HMC_vs_Metro 3 -2.643 0.0131 -0.482
HMC_vs_Metro 4 -0.437 0.665 -0.080
HMC_vs_Metro 5 0.519 0.608 0.095
Metro_vs_DEMetro_Z 0 0.356 0.725 0.065
Metro_vs_DEMetro_Z 1 -4.459 0.000114 -0.814
Metro_vs_DEMetro_Z 2 -7.665 1.88e-08 -1.399
Metro_vs_DEMetro_Z 3 -14.110 1.61e-14 -2.576
Metro_vs_DEMetro_Z 4 -23.461 2.08e-20 -4.283
Metro_vs_DEMetro_Z 5 -38.651 1.69e-26 -7.057
HMC_vs_SMC 0 2.412 0.0224 0.440
HMC_vs_SMC 1 -5.863 2.32e-06 -1.070
HMC_vs_SMC 2 -21.712 1.75e-19 -3.964
HMC_vs_SMC 3 -28.905 6.25e-23 -5.277
HMC_vs_SMC 4 -12.179 6.32e-13 -2.223
HMC_vs_SMC 5 -8.210 4.72e-09 -1.499
Metro_vs_SMC 0 8.238 4.4e-09 1.504
Metro_vs_SMC 1 -2.349 0.0258 -0.429
Metro_vs_SMC 2 -19.143 5.36e-18 -3.495
Metro_vs_SMC 3 -28.520 9.1e-23 -5.207
Metro_vs_SMC 4 -25.099 3.22e-21 -4.582
Metro_vs_SMC 5 -31.883 3.96e-24 -5.821
HMC_vs_DEMetro_Z 0 -6.732 2.19e-07 -1.229
HMC_vs_DEMetro_Z 1 -5.771 2.99e-06 -1.054
HMC_vs_DEMetro_Z 2 -8.423 2.78e-09 -1.538
HMC_vs_DEMetro_Z 3 -13.874 2.47e-14 -2.533
HMC_vs_DEMetro_Z 4 -14.434 9.02e-15 -2.635
HMC_vs_DEMetro_Z 5 -11.305 3.8e-12 -2.064
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.020 0.015 0.005 1.089
HMC 3 0.020 0.015 0.003 1.404
HMC 5 0.019 0.014 0.002 2.218
HMC 8 0.027 0.015 0.002 5.533
HMC 15 0.084 0.015 0.002 34.188
HMC 30 0.115 0.016 0.002 47.294
SMC 2 0.016 0.015 0.005 0.221
SMC 3 0.047 0.015 0.003 9.064
SMC 5 0.211 0.014 0.002 88.696
SMC 8 0.332 0.015 0.002 140.193
SMC 15 0.400 0.015 0.002 190.517
SMC 30 0.407 0.016 0.002 186.557
Metro 2 0.035 0.015 0.005 4.454
Metro 3 0.035 0.015 0.003 5.796
Metro 5 0.043 0.014 0.002 12.970
Metro 8 0.043 0.015 0.002 12.191
Metro 15 0.097 0.015 0.002 40.552
Metro 30 0.096 0.016 0.002 38.157
DEMetro_Z 2 0.034 0.015 0.005 4.190
DEMetro_Z 3 0.091 0.015 0.003 21.848
DEMetro_Z 5 0.229 0.014 0.002 96.839
DEMetro_Z 8 0.314 0.015 0.002 132.368
DEMetro_Z 15 0.506 0.015 0.002 242.889
DEMetro_Z 30 0.537 0.016 0.002 248.741
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
Forest & Ridge Plots
Pooled
2 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
8 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
15 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
30 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
8 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
15 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
30 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2
3
5
8
15
30
Chain
2
3
5
8
15
30

Vary_Dimension_with_high_Multimodality (Mixture, dimension, 30 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 5.931 1.87e-06 17.932
HMC 3 6.787 1.83e-07 23.505
HMC 5 6.380 5.47e-07 20.254
HMC 8 6.620 2.91e-07 30.390
HMC 15 7.114 7.75e-08 30.750
HMC 30 6.543 3.61e-07 44.752
SMC 2 0.114 0.91 0.027
SMC 3 -0.407 0.686 -0.103
SMC 5 -0.877 0.384 -0.211
SMC 8 0.077 0.939 0.020
SMC 15 -0.239 0.812 -0.061
SMC 30 0.410 0.683 0.118
Metro 2 6.883 1.3e-07 12.289
Metro 3 5.919 1.82e-06 9.959
Metro 5 7.011 8.97e-08 11.117
Metro 8 5.452 7.04e-06 15.473
Metro 15 5.589 4.78e-06 14.662
Metro 30 6.856 1.5e-07 18.475
DEMetro_Z 2 7.455 2.79e-08 12.470
DEMetro_Z 3 7.582 2.23e-08 23.627
DEMetro_Z 5 15.632 1.12e-15 101.051
DEMetro_Z 8 19.561 2.97e-18 309.818
DEMetro_Z 15 31.532 5.35e-24 515.846
DEMetro_Z 30 43.506 5.75e-28 1186.177
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 1.633 0.113 0.298
HMC_vs_DEMetro_Z 1 -0.024 0.981 -0.004
HMC_vs_DEMetro_Z 2 -10.873 9.55e-12 -1.985
HMC_vs_DEMetro_Z 3 -16.098 5.36e-16 -2.939
HMC_vs_DEMetro_Z 4 -30.305 1.65e-23 -5.533
HMC_vs_DEMetro_Z 5 -40.525 4.38e-27 -7.399
Metro_vs_SMC 0 6.862 1.54e-07 1.253
Metro_vs_SMC 1 5.988 1.65e-06 1.093
Metro_vs_SMC 2 7.161 7e-08 1.307
Metro_vs_SMC 3 5.559 5.37e-06 1.015
Metro_vs_SMC 4 5.719 3.45e-06 1.044
Metro_vs_SMC 5 6.923 1.31e-07 1.264
Metro_vs_DEMetro_Z 0 -0.065 0.948 -0.012
Metro_vs_DEMetro_Z 1 -3.810 0.000669 -0.696
Metro_vs_DEMetro_Z 2 -13.040 1.17e-13 -2.381
Metro_vs_DEMetro_Z 3 -17.744 4.09e-17 -3.240
Metro_vs_DEMetro_Z 4 -31.310 6.6e-24 -5.716
Metro_vs_DEMetro_Z 5 -41.574 2.11e-27 -7.590
HMC_vs_Metro 0 1.637 0.112 0.299
HMC_vs_Metro 1 3.784 0.000718 0.691
HMC_vs_Metro 2 3.023 0.0052 0.552
HMC_vs_Metro 3 2.890 0.00722 0.528
HMC_vs_Metro 4 3.591 0.0012 0.656
HMC_vs_Metro 5 3.493 0.00155 0.638
HMC_vs_SMC 0 5.928 1.94e-06 1.082
HMC_vs_SMC 1 6.816 1.75e-07 1.244
HMC_vs_SMC 2 6.433 4.89e-07 1.175
HMC_vs_SMC 3 6.574 3.34e-07 1.200
HMC_vs_SMC 4 7.132 7.55e-08 1.302
HMC_vs_SMC 5 6.566 3.41e-07 1.199
DEMetro_Z_vs_SMC 0 7.536 2.63e-08 1.376
DEMetro_Z_vs_SMC 1 7.526 2.69e-08 1.374
DEMetro_Z_vs_SMC 2 15.628 1.16e-15 2.853
DEMetro_Z_vs_SMC 3 19.520 3.17e-18 3.564
DEMetro_Z_vs_SMC 4 31.578 5.18e-24 5.765
DEMetro_Z_vs_SMC 5 43.451 5.98e-28 7.933
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.774 0.058 0.040 17.932
HMC 3 0.835 0.052 0.033 23.505
HMC 5 0.548 0.041 0.025 20.254
HMC 8 0.507 0.035 0.016 30.390
HMC 15 0.388 0.032 0.012 30.750
HMC 30 0.286 0.028 0.006 44.752
SMC 2 0.059 0.058 0.040 0.027
SMC 3 0.049 0.052 0.033 -0.103
SMC 5 0.036 0.041 0.025 -0.211
SMC 8 0.036 0.035 0.016 0.020
SMC 15 0.031 0.032 0.012 -0.061
SMC 30 0.028 0.028 0.006 0.118
Metro 2 0.549 0.058 0.040 12.289
Metro 3 0.384 0.052 0.033 9.959
Metro 5 0.319 0.041 0.025 11.117
Metro 8 0.276 0.035 0.016 15.473
Metro 15 0.202 0.032 0.012 14.662
Metro 30 0.134 0.028 0.006 18.475
DEMetro_Z 2 0.556 0.058 0.040 12.470
DEMetro_Z 3 0.839 0.052 0.033 23.627
DEMetro_Z 5 2.568 0.041 0.025 101.051
DEMetro_Z 8 4.846 0.035 0.016 309.818
DEMetro_Z 15 6.012 0.032 0.012 515.846
DEMetro_Z 30 6.865 0.028 0.006 1186.177
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 3.475 0.00162 18.712
HMC 3 4.137 0.000275 39.514
HMC 5 3.908 0.000512 29.043
HMC 8 4.339 0.000157 22.068
HMC 15 4.309 0.000171 22.348
HMC 30 4.278 0.000187 62.215
SMC 2 2.139 0.0369 0.648
SMC 3 0.963 0.339 0.269
SMC 5 0.507 0.615 0.194
SMC 8 -1.355 0.182 -0.293
SMC 15 -1.102 0.275 -0.254
SMC 30 3.984 0.000238 1.461
Metro 2 4.339 0.000152 7.459
Metro 3 4.206 0.000222 8.290
Metro 5 4.172 0.000245 9.253
Metro 8 3.428 0.00182 6.864
Metro 15 3.426 0.00181 5.645
Metro 30 5.507 5.9e-06 11.322
DEMetro_Z 2 4.285 0.000176 7.234
DEMetro_Z 3 5.271 1.19e-05 44.355
DEMetro_Z 5 9.933 7.68e-11 1234.192
DEMetro_Z 8 13.243 7.97e-14 1926.413
DEMetro_Z 15 21.902 1.38e-19 3800.701
DEMetro_Z 30 45.523 1.58e-28 14531.322
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 3.336 0.00234 0.609
HMC_vs_SMC 1 4.099 0.000306 0.748
HMC_vs_SMC 2 3.860 0.000584 0.705
HMC_vs_SMC 3 4.427 0.000124 0.808
HMC_vs_SMC 4 4.352 0.000153 0.795
HMC_vs_SMC 5 4.192 0.000237 0.765
Metro_vs_DEMetro_Z 0 0.082 0.935 0.015
Metro_vs_DEMetro_Z 1 -4.053 0.000347 -0.740
Metro_vs_DEMetro_Z 2 -9.858 9.13e-11 -1.800
Metro_vs_DEMetro_Z 3 -13.159 9.34e-14 -2.403
Metro_vs_DEMetro_Z 4 -21.858 1.46e-19 -3.991
Metro_vs_DEMetro_Z 5 -45.499 1.6e-28 -8.307
HMC_vs_Metro 0 2.008 0.054 0.367
HMC_vs_Metro 1 3.344 0.00229 0.611
HMC_vs_Metro 2 2.864 0.00771 0.523
HMC_vs_Metro 3 2.851 0.00795 0.521
HMC_vs_Metro 4 3.399 0.00199 0.620
HMC_vs_Metro 5 3.423 0.00187 0.625
HMC_vs_DEMetro_Z 0 2.039 0.0506 0.372
HMC_vs_DEMetro_Z 1 -0.357 0.724 -0.065
HMC_vs_DEMetro_Z 2 -9.621 1.57e-10 -1.757
HMC_vs_DEMetro_Z 3 -13.003 1.26e-13 -2.374
HMC_vs_DEMetro_Z 4 -21.678 1.83e-19 -3.958
HMC_vs_DEMetro_Z 5 -45.084 2.08e-28 -8.231
Metro_vs_SMC 0 4.060 0.00034 0.741
Metro_vs_SMC 1 3.992 0.000409 0.729
Metro_vs_SMC 2 3.996 0.000404 0.730
Metro_vs_SMC 3 3.534 0.00139 0.645
Metro_vs_SMC 4 3.594 0.00119 0.656
Metro_vs_SMC 5 4.599 7.71e-05 0.840
DEMetro_Z_vs_SMC 0 3.900 0.000524 0.712
DEMetro_Z_vs_SMC 1 5.195 1.48e-05 0.948
DEMetro_Z_vs_SMC 2 9.931 7.72e-11 1.813
DEMetro_Z_vs_SMC 3 13.248 7.9e-14 2.419
DEMetro_Z_vs_SMC 4 21.908 1.37e-19 4.000
DEMetro_Z_vs_SMC 5 45.530 1.57e-28 8.313
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 1.455 0.091 0.073 18.712
HMC 3 1.871 0.072 0.046 39.514
HMC 5 1.078 0.071 0.035 29.043
HMC 8 1.140 0.074 0.048 22.068
HMC 15 0.870 0.061 0.036 22.348
HMC 30 0.725 0.041 0.011 62.215
SMC 2 0.138 0.091 0.073 0.648
SMC 3 0.085 0.072 0.046 0.269
SMC 5 0.078 0.071 0.035 0.194
SMC 8 0.060 0.074 0.048 -0.293
SMC 15 0.052 0.061 0.036 -0.254
SMC 30 0.058 0.041 0.011 1.461
Metro 2 0.635 0.091 0.073 7.459
Metro 3 0.450 0.072 0.046 8.290
Metro 5 0.392 0.071 0.035 9.253
Metro 8 0.406 0.074 0.048 6.864
Metro 15 0.265 0.061 0.036 5.645
Metro 30 0.166 0.041 0.011 11.322
DEMetro_Z 2 0.618 0.091 0.073 7.234
DEMetro_Z 3 2.091 0.072 0.046 44.355
DEMetro_Z 5 42.868 0.071 0.035 1234.192
DEMetro_Z 8 93.082 0.074 0.048 1926.413
DEMetro_Z 15 137.656 0.061 0.036 3800.701
DEMetro_Z 30 159.635 0.041 0.011 14531.322
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 5.891 2.1e-06 20.456
HMC 3 6.727 2.16e-07 26.127
HMC 5 6.371 5.65e-07 22.993
HMC 8 6.670 2.56e-07 38.183
HMC 15 6.748 2.07e-07 40.921
HMC 30 6.316 6.7e-07 58.770
SMC 2 0.126 0.9 0.030
SMC 3 -0.052 0.959 -0.013
SMC 5 -0.930 0.357 -0.222
SMC 8 -0.385 0.702 -0.101
SMC 15 -0.289 0.773 -0.072
SMC 30 1.260 0.213 0.369
Metro 2 6.871 1.39e-07 14.381
Metro 3 5.882 2.06e-06 11.238
Metro 5 6.746 1.88e-07 11.634
Metro 8 5.507 6.09e-06 19.002
Metro 15 5.656 4.02e-06 18.754
Metro 30 6.931 1.25e-07 23.462
DEMetro_Z 2 7.567 2.17e-08 14.831
DEMetro_Z 3 7.764 1.4e-08 26.353
DEMetro_Z 5 16.134 5e-16 185.769
DEMetro_Z 8 22.290 8.52e-20 688.574
DEMetro_Z 15 40.598 4.15e-27 1264.014
DEMetro_Z 30 87.713 9.96e-37 2878.778
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -0.137 0.892 -0.025
Metro_vs_DEMetro_Z 1 -3.820 0.00065 -0.697
Metro_vs_DEMetro_Z 2 -14.969 3.54e-15 -2.733
Metro_vs_DEMetro_Z 3 -20.927 4.79e-19 -3.821
Metro_vs_DEMetro_Z 4 -40.001 6.34e-27 -7.303
Metro_vs_DEMetro_Z 5 -84.423 3.02e-36 -15.414
DEMetro_Z_vs_SMC 0 7.634 2.04e-08 1.394
DEMetro_Z_vs_SMC 1 7.677 1.83e-08 1.402
DEMetro_Z_vs_SMC 2 16.116 5.2e-16 2.942
DEMetro_Z_vs_SMC 3 22.278 8.65e-20 4.067
DEMetro_Z_vs_SMC 4 40.625 4.08e-27 7.417
DEMetro_Z_vs_SMC 5 87.777 9.79e-37 16.026
HMC_vs_DEMetro_Z 0 1.483 0.149 0.271
HMC_vs_DEMetro_Z 1 -0.039 0.969 -0.007
HMC_vs_DEMetro_Z 2 -13.275 7.5e-14 -2.424
HMC_vs_DEMetro_Z 3 -19.624 2.75e-18 -3.583
HMC_vs_DEMetro_Z 4 -37.962 2.81e-26 -6.931
HMC_vs_DEMetro_Z 5 -84.529 2.91e-36 -15.433
HMC_vs_Metro 0 1.532 0.136 0.280
HMC_vs_Metro 1 3.677 0.000954 0.671
HMC_vs_Metro 2 3.259 0.00286 0.595
HMC_vs_Metro 3 2.999 0.00551 0.548
HMC_vs_Metro 4 3.640 0.00105 0.665
HMC_vs_Metro 5 3.479 0.00161 0.635
HMC_vs_SMC 0 5.872 2.27e-06 1.072
HMC_vs_SMC 1 6.741 2.13e-07 1.231
HMC_vs_SMC 2 6.425 4.99e-07 1.173
HMC_vs_SMC 3 6.656 2.68e-07 1.215
HMC_vs_SMC 4 6.766 2e-07 1.235
HMC_vs_SMC 5 6.308 6.87e-07 1.152
Metro_vs_SMC 0 6.870 1.51e-07 1.254
Metro_vs_SMC 1 5.884 2.19e-06 1.074
Metro_vs_SMC 2 6.885 1.45e-07 1.257
Metro_vs_SMC 3 5.632 4.38e-06 1.028
Metro_vs_SMC 4 5.758 3.1e-06 1.051
Metro_vs_SMC 5 6.884 1.46e-07 1.257
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.686 0.069 0.030 20.456
HMC 3 0.723 0.059 0.025 26.127
HMC 5 0.482 0.050 0.019 22.993
HMC 8 0.429 0.043 0.010 38.183
HMC 15 0.324 0.038 0.007 40.921
HMC 30 0.236 0.034 0.003 58.770
SMC 2 0.070 0.069 0.030 0.030
SMC 3 0.059 0.059 0.025 -0.013
SMC 5 0.045 0.050 0.019 -0.222
SMC 8 0.042 0.043 0.010 -0.101
SMC 15 0.038 0.038 0.007 -0.072
SMC 30 0.035 0.034 0.003 0.369
Metro 2 0.502 0.069 0.030 14.381
Metro 3 0.345 0.059 0.025 11.238
Metro 5 0.268 0.050 0.019 11.634
Metro 8 0.235 0.043 0.010 19.002
Metro 15 0.169 0.038 0.007 18.754
Metro 30 0.115 0.034 0.003 23.462
DEMetro_Z 2 0.516 0.069 0.030 14.831
DEMetro_Z 3 0.729 0.059 0.025 26.353
DEMetro_Z 5 3.543 0.050 0.019 185.769
DEMetro_Z 8 7.007 0.043 0.010 688.574
DEMetro_Z 15 8.877 0.038 0.007 1264.014
DEMetro_Z 30 9.945 0.034 0.003 2878.778
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 5.829 2.51e-06 22.728
HMC 3 6.705 2.3e-07 25.979
HMC 5 6.208 8.83e-07 22.790
HMC 8 6.548 3.55e-07 36.099
HMC 15 6.846 1.59e-07 35.716
HMC 30 6.566 3.39e-07 50.157
SMC 2 0.694 0.491 0.172
SMC 3 -0.203 0.84 -0.048
SMC 5 -1.037 0.304 -0.251
SMC 8 -0.179 0.859 -0.048
SMC 15 -0.304 0.762 -0.078
SMC 30 1.376 0.174 0.416
Metro 2 6.835 1.55e-07 15.284
Metro 3 5.977 1.57e-06 10.814
Metro 5 6.764 1.82e-07 12.563
Metro 8 5.357 9.25e-06 18.086
Metro 15 5.443 7.25e-06 16.885
Metro 30 6.943 1.2e-07 21.285
DEMetro_Z 2 7.311 4.33e-08 15.866
DEMetro_Z 3 7.169 6.62e-08 24.396
DEMetro_Z 5 29.557 2.12e-23 68.333
DEMetro_Z 8 70.922 1.28e-34 126.627
DEMetro_Z 15 71.524 1.28e-34 142.123
DEMetro_Z 30 122.029 2.05e-41 247.740
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 7.318 4.63e-08 1.336
DEMetro_Z_vs_SMC 1 7.118 7.84e-08 1.300
DEMetro_Z_vs_SMC 2 29.219 4.61e-23 5.335
DEMetro_Z_vs_SMC 3 70.238 6.1e-34 12.824
DEMetro_Z_vs_SMC 4 72.514 2.43e-34 13.239
DEMetro_Z_vs_SMC 5 121.028 9.04e-41 22.097
HMC_vs_Metro 0 1.690 0.102 0.309
HMC_vs_Metro 1 3.794 0.000697 0.693
HMC_vs_Metro 2 2.895 0.00714 0.528
HMC_vs_Metro 3 2.913 0.00682 0.532
HMC_vs_Metro 4 3.506 0.0015 0.640
HMC_vs_Metro 5 3.464 0.00168 0.632
Metro_vs_DEMetro_Z 0 -0.166 0.87 -0.030
Metro_vs_DEMetro_Z 1 -3.530 0.00141 -0.644
Metro_vs_DEMetro_Z 2 -19.696 2.49e-18 -3.596
Metro_vs_DEMetro_Z 3 -28.460 9.65e-23 -5.196
Metro_vs_DEMetro_Z 4 -46.017 1.16e-28 -8.402
Metro_vs_DEMetro_Z 5 -62.283 1.95e-32 -11.371
HMC_vs_SMC 0 5.789 2.84e-06 1.057
HMC_vs_SMC 1 6.713 2.3e-07 1.226
HMC_vs_SMC 2 6.265 7.72e-07 1.144
HMC_vs_SMC 3 6.514 3.93e-07 1.189
HMC_vs_SMC 4 6.876 1.49e-07 1.255
HMC_vs_SMC 5 6.560 3.47e-07 1.198
Metro_vs_SMC 0 6.800 1.82e-07 1.242
Metro_vs_SMC 1 6.015 1.53e-06 1.098
Metro_vs_SMC 2 6.906 1.37e-07 1.261
Metro_vs_SMC 3 5.459 7.09e-06 0.997
Metro_vs_SMC 4 5.556 5.41e-06 1.014
Metro_vs_SMC 5 6.881 1.47e-07 1.256
HMC_vs_DEMetro_Z 0 1.600 0.12 0.292
HMC_vs_DEMetro_Z 1 0.277 0.784 0.051
HMC_vs_DEMetro_Z 2 -10.539 1.98e-11 -1.924
HMC_vs_DEMetro_Z 3 -16.940 1.4e-16 -3.093
HMC_vs_DEMetro_Z 4 -20.642 6.96e-19 -3.769
HMC_vs_DEMetro_Z 5 -25.947 1.28e-21 -4.737
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.167 0.013 0.007 22.728
HMC 3 0.214 0.014 0.008 25.979
HMC 5 0.165 0.014 0.007 22.790
HMC 8 0.179 0.014 0.005 36.099
HMC 15 0.159 0.014 0.004 35.716
HMC 30 0.129 0.014 0.002 50.157
SMC 2 0.014 0.013 0.007 0.172
SMC 3 0.013 0.014 0.008 -0.048
SMC 5 0.012 0.014 0.007 -0.251
SMC 8 0.014 0.014 0.005 -0.048
SMC 15 0.014 0.014 0.004 -0.078
SMC 30 0.015 0.014 0.002 0.416
Metro 2 0.117 0.013 0.007 15.284
Metro 3 0.097 0.014 0.008 10.814
Metro 5 0.097 0.014 0.007 12.563
Metro 8 0.096 0.014 0.005 18.086
Metro 15 0.083 0.014 0.004 16.885
Metro 30 0.063 0.014 0.002 21.285
DEMetro_Z 2 0.121 0.013 0.007 15.866
DEMetro_Z 3 0.201 0.014 0.008 24.396
DEMetro_Z 5 0.468 0.014 0.007 68.333
DEMetro_Z 8 0.592 0.014 0.005 126.627
DEMetro_Z 15 0.589 0.014 0.004 142.123
DEMetro_Z 30 0.580 0.014 0.002 247.740
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 8.352 3.24e-09 40.878
HMC 3 7.828 1.22e-08 38.736
HMC 5 8.779 1.13e-09 41.988
HMC 8 9.981 6.76e-11 60.582
HMC 15 9.277 3.45e-10 52.155
HMC 30 8.644 1.6e-09 69.149
SMC 2 -0.642 0.524 -0.148
SMC 3 -1.487 0.143 -0.344
SMC 5 -1.023 0.311 -0.233
SMC 8 -0.828 0.411 -0.201
SMC 15 -0.847 0.401 -0.195
SMC 30 1.480 0.145 0.448
Metro 2 6.334 5.93e-07 12.532
Metro 3 5.979 1.55e-06 10.683
Metro 5 7.316 3.98e-08 11.656
Metro 8 6.907 1.26e-07 14.236
Metro 15 8.360 2.67e-09 13.637
Metro 30 5.716 3.4e-06 17.867
DEMetro_Z 2 4.272 0.000183 7.504
DEMetro_Z 3 6.176 9.7e-07 28.645
DEMetro_Z 5 10.722 1.3e-11 71.393
DEMetro_Z 8 11.365 3.35e-12 392.464
DEMetro_Z 15 18.228 2e-17 776.310
DEMetro_Z 30 32.418 2.47e-24 1934.906
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 6.545 3.61e-07 1.195
HMC_vs_DEMetro_Z 1 1.598 0.121 0.292
HMC_vs_DEMetro_Z 2 -3.650 0.00103 -0.666
HMC_vs_DEMetro_Z 3 -9.656 1.45e-10 -1.763
HMC_vs_DEMetro_Z 4 -16.754 1.88e-16 -3.059
HMC_vs_DEMetro_Z 5 -30.224 1.78e-23 -5.518
Metro_vs_SMC 0 6.294 7.13e-07 1.149
Metro_vs_SMC 1 6.117 1.16e-06 1.117
Metro_vs_SMC 2 7.340 4.37e-08 1.340
Metro_vs_SMC 3 6.990 1.1e-07 1.276
Metro_vs_SMC 4 8.649 1.6e-09 1.579
Metro_vs_SMC 5 5.508 6.19e-06 1.006
Metro_vs_DEMetro_Z 0 1.954 0.0604 0.357
Metro_vs_DEMetro_Z 1 -3.759 0.000766 -0.686
Metro_vs_DEMetro_Z 2 -9.041 6.18e-10 -1.651
Metro_vs_DEMetro_Z 3 -10.948 8.14e-12 -1.999
Metro_vs_DEMetro_Z 4 -18.224 2.01e-17 -3.327
Metro_vs_DEMetro_Z 5 -32.200 2.99e-24 -5.879
HMC_vs_Metro 0 5.180 1.54e-05 0.946
HMC_vs_Metro 1 5.044 2.24e-05 0.921
HMC_vs_Metro 2 5.690 3.74e-06 1.039
HMC_vs_Metro 3 6.704 2.35e-07 1.224
HMC_vs_Metro 4 6.327 6.52e-07 1.155
HMC_vs_Metro 5 5.605 4.72e-06 1.023
HMC_vs_SMC 0 8.341 3.4e-09 1.523
HMC_vs_SMC 1 7.928 9.63e-09 1.447
HMC_vs_SMC 2 8.858 9.59e-10 1.617
HMC_vs_SMC 3 9.985 6.82e-11 1.823
HMC_vs_SMC 4 9.179 4.44e-10 1.676
HMC_vs_SMC 5 8.626 1.69e-09 1.575
DEMetro_Z_vs_SMC 0 4.342 0.000157 0.793
DEMetro_Z_vs_SMC 1 6.238 8.3e-07 1.139
DEMetro_Z_vs_SMC 2 10.709 1.36e-11 1.955
DEMetro_Z_vs_SMC 3 11.382 3.24e-12 2.078
DEMetro_Z_vs_SMC 4 18.242 1.95e-17 3.331
DEMetro_Z_vs_SMC 5 32.415 2.48e-24 5.918
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 1.691 0.058 0.040 40.878
HMC 3 1.342 0.052 0.033 38.736
HMC 5 1.091 0.041 0.025 41.988
HMC 8 0.976 0.035 0.016 60.582
HMC 15 0.636 0.032 0.012 52.155
HMC 30 0.426 0.028 0.006 69.149
SMC 2 0.052 0.058 0.040 -0.148
SMC 3 0.041 0.052 0.033 -0.344
SMC 5 0.035 0.041 0.025 -0.233
SMC 8 0.032 0.035 0.016 -0.201
SMC 15 0.030 0.032 0.012 -0.195
SMC 30 0.030 0.028 0.006 0.448
Metro 2 0.559 0.058 0.040 12.532
Metro 3 0.408 0.052 0.033 10.683
Metro 5 0.333 0.041 0.025 11.656
Metro 8 0.256 0.035 0.016 14.236
Metro 15 0.190 0.032 0.012 13.637
Metro 30 0.131 0.028 0.006 17.867
DEMetro_Z 2 0.358 0.058 0.040 7.504
DEMetro_Z 3 1.006 0.052 0.033 28.645
DEMetro_Z 5 1.826 0.041 0.025 71.393
DEMetro_Z 8 6.129 0.035 0.016 392.464
DEMetro_Z 15 9.031 0.032 0.012 776.310
DEMetro_Z 30 11.181 0.028 0.006 1934.906
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 6.157 1.03e-06 75.732
HMC 3 5.811 2.67e-06 96.233
HMC 5 6.205 9.08e-07 100.668
HMC 8 7.342 4.33e-08 70.065
HMC 15 6.538 3.66e-07 54.711
HMC 30 5.995 1.61e-06 117.368
SMC 2 -0.028 0.978 -0.007
SMC 3 2.013 0.0493 0.642
SMC 5 0.875 0.386 0.257
SMC 8 -1.610 0.114 -0.354
SMC 15 -1.226 0.226 -0.265
SMC 30 1.899 0.0634 0.639
Metro 2 4.368 0.000142 8.966
Metro 3 3.450 0.00172 8.771
Metro 5 3.484 0.00157 7.907
Metro 8 3.740 0.000768 4.696
Metro 15 5.379 6.1e-06 3.916
Metro 30 3.710 0.000868 12.253
DEMetro_Z 2 3.616 0.00109 5.835
DEMetro_Z 3 4.444 0.000118 63.657
DEMetro_Z 5 4.932 3.06e-05 290.759
DEMetro_Z 8 9.831 9.69e-11 471.111
DEMetro_Z 15 15.229 2.27e-15 512.351
DEMetro_Z 30 14.302 1.14e-14 1807.703
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 6.155 1.04e-06 1.124
HMC_vs_SMC 1 5.754 3.13e-06 1.051
HMC_vs_SMC 2 6.206 9.06e-07 1.133
HMC_vs_SMC 3 7.368 4.07e-08 1.345
HMC_vs_SMC 4 6.565 3.42e-07 1.199
HMC_vs_SMC 5 5.973 1.72e-06 1.090
Metro_vs_DEMetro_Z 0 1.215 0.234 0.222
Metro_vs_DEMetro_Z 1 -3.848 0.000604 -0.702
Metro_vs_DEMetro_Z 2 -4.770 4.81e-05 -0.871
Metro_vs_DEMetro_Z 3 -9.754 1.16e-10 -1.781
Metro_vs_DEMetro_Z 4 -15.203 2.37e-15 -2.776
Metro_vs_DEMetro_Z 5 -14.172 1.44e-14 -2.587
HMC_vs_Metro 0 5.317 1.05e-05 0.971
HMC_vs_Metro 1 5.090 1.97e-05 0.929
HMC_vs_Metro 2 5.464 7e-06 0.998
HMC_vs_Metro 3 6.559 3.48e-07 1.198
HMC_vs_Metro 4 5.978 1.69e-06 1.092
HMC_vs_Metro 5 5.163 1.61e-05 0.943
HMC_vs_DEMetro_Z 0 5.865 2.31e-06 1.071
HMC_vs_DEMetro_Z 1 1.608 0.119 0.294
HMC_vs_DEMetro_Z 2 -3.243 0.00298 -0.592
HMC_vs_DEMetro_Z 3 -8.245 4.33e-09 -1.505
HMC_vs_DEMetro_Z 4 -13.731 3.21e-14 -2.507
HMC_vs_DEMetro_Z 5 -13.463 5.27e-14 -2.458
Metro_vs_SMC 0 4.433 0.000122 0.809
Metro_vs_SMC 1 3.152 0.00375 0.575
Metro_vs_SMC 2 3.299 0.00258 0.602
Metro_vs_SMC 3 4.009 0.00039 0.732
Metro_vs_SMC 4 5.788 2.86e-06 1.057
Metro_vs_SMC 5 3.508 0.00149 0.640
DEMetro_Z_vs_SMC 0 3.688 0.000928 0.673
DEMetro_Z_vs_SMC 1 4.413 0.000129 0.806
DEMetro_Z_vs_SMC 2 4.932 3.06e-05 0.900
DEMetro_Z_vs_SMC 3 9.841 9.48e-11 1.797
DEMetro_Z_vs_SMC 4 15.239 2.23e-15 2.782
DEMetro_Z_vs_SMC 5 14.311 1.12e-14 2.613
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 5.613 0.091 0.073 75.732
HMC 3 4.453 0.072 0.046 96.233
HMC 5 3.562 0.071 0.035 100.668
HMC 8 3.457 0.074 0.048 70.065
HMC 15 2.041 0.061 0.036 54.711
HMC 30 1.330 0.041 0.011 117.368
SMC 2 0.090 0.091 0.073 -0.007
SMC 3 0.102 0.072 0.046 0.642
SMC 5 0.080 0.071 0.035 0.257
SMC 8 0.057 0.074 0.048 -0.354
SMC 15 0.051 0.061 0.036 -0.265
SMC 30 0.048 0.041 0.011 0.639
Metro 2 0.744 0.091 0.073 8.966
Metro 3 0.472 0.072 0.046 8.771
Metro 5 0.345 0.071 0.035 7.907
Metro 8 0.301 0.074 0.048 4.696
Metro 15 0.202 0.061 0.036 3.916
Metro 30 0.176 0.041 0.011 12.253
DEMetro_Z 2 0.516 0.091 0.073 5.835
DEMetro_Z 3 2.970 0.072 0.046 63.657
DEMetro_Z 5 10.153 0.071 0.035 290.759
DEMetro_Z 8 22.820 0.074 0.048 471.111
DEMetro_Z 15 18.609 0.061 0.036 512.351
DEMetro_Z 30 19.895 0.041 0.011 1807.703
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 8.285 3.85e-09 47.192
HMC 3 7.912 9.86e-09 43.024
HMC 5 8.694 1.4e-09 44.742
HMC 8 9.728 1.22e-10 74.423
HMC 15 8.844 9.82e-10 70.024
HMC 30 8.381 3.07e-09 90.289
SMC 2 -0.632 0.53 -0.147
SMC 3 -1.148 0.256 -0.257
SMC 5 -1.104 0.275 -0.247
SMC 8 -1.183 0.242 -0.275
SMC 15 -0.559 0.579 -0.132
SMC 30 1.866 0.0675 0.564
Metro 2 6.252 7.6e-07 14.887
Metro 3 5.888 2.04e-06 12.099
Metro 5 7.239 4.99e-08 12.463
Metro 8 6.948 1.16e-07 17.561
Metro 15 8.531 1.86e-09 16.923
Metro 30 5.755 3.08e-06 22.418
DEMetro_Z 2 4.551 8.55e-05 9.336
DEMetro_Z 3 6.353 6e-07 31.823
DEMetro_Z 5 10.627 1.61e-11 85.833
DEMetro_Z 8 11.815 1.32e-12 518.211
DEMetro_Z 15 18.331 1.72e-17 1090.155
DEMetro_Z 30 33.227 1.23e-24 2683.139
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 1.795 0.0831 0.328
Metro_vs_DEMetro_Z 1 -3.815 0.00066 -0.696
Metro_vs_DEMetro_Z 2 -9.039 6.2e-10 -1.650
Metro_vs_DEMetro_Z 3 -11.403 3.1e-12 -2.082
Metro_vs_DEMetro_Z 4 -18.327 1.73e-17 -3.346
Metro_vs_DEMetro_Z 5 -33.028 1.46e-24 -6.030
DEMetro_Z_vs_SMC 0 4.612 7.44e-05 0.842
DEMetro_Z_vs_SMC 1 6.407 5.25e-07 1.170
DEMetro_Z_vs_SMC 2 10.630 1.62e-11 1.941
DEMetro_Z_vs_SMC 3 11.828 1.29e-12 2.159
DEMetro_Z_vs_SMC 4 18.339 1.7e-17 3.348
DEMetro_Z_vs_SMC 5 33.217 1.24e-24 6.065
HMC_vs_DEMetro_Z 0 6.466 4.47e-07 1.181
HMC_vs_DEMetro_Z 1 1.593 0.122 0.291
HMC_vs_DEMetro_Z 2 -4.213 0.000224 -0.769
HMC_vs_DEMetro_Z 3 -10.077 5.55e-11 -1.840
HMC_vs_DEMetro_Z 4 -16.782 1.8e-16 -3.064
HMC_vs_DEMetro_Z 5 -31.113 7.88e-24 -5.680
HMC_vs_Metro 0 5.042 2.26e-05 0.921
HMC_vs_Metro 1 5.011 2.46e-05 0.915
HMC_vs_Metro 2 5.672 3.94e-06 1.035
HMC_vs_Metro 3 6.574 3.34e-07 1.200
HMC_vs_Metro 4 6.349 6.14e-07 1.159
HMC_vs_Metro 5 5.563 5.31e-06 1.016
HMC_vs_SMC 0 8.285 3.91e-09 1.513
HMC_vs_SMC 1 7.982 8.39e-09 1.457
HMC_vs_SMC 2 8.779 1.16e-09 1.603
HMC_vs_SMC 3 9.741 1.19e-10 1.778
HMC_vs_SMC 4 8.775 1.17e-09 1.602
HMC_vs_SMC 5 8.372 3.16e-09 1.528
Metro_vs_SMC 0 6.206 9.05e-07 1.133
Metro_vs_SMC 1 6.017 1.52e-06 1.099
Metro_vs_SMC 2 7.286 5.03e-08 1.330
Metro_vs_SMC 3 7.059 9.16e-08 1.289
Metro_vs_SMC 4 8.733 1.3e-09 1.594
Metro_vs_SMC 5 5.540 5.66e-06 1.011
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 1.492 0.069 0.030 47.192
HMC 3 1.152 0.059 0.025 43.024
HMC 5 0.891 0.050 0.019 44.742
HMC 8 0.796 0.043 0.010 74.423
HMC 15 0.528 0.038 0.007 70.024
HMC 30 0.345 0.034 0.003 90.289
SMC 2 0.064 0.069 0.030 -0.147
SMC 3 0.053 0.059 0.025 -0.257
SMC 5 0.045 0.050 0.019 -0.247
SMC 8 0.040 0.043 0.010 -0.275
SMC 15 0.037 0.038 0.007 -0.132
SMC 30 0.036 0.034 0.003 0.564
Metro 2 0.518 0.069 0.030 14.887
Metro 3 0.367 0.059 0.025 12.099
Metro 5 0.284 0.050 0.019 12.463
Metro 8 0.221 0.043 0.010 17.561
Metro 15 0.157 0.038 0.007 16.923
Metro 30 0.111 0.034 0.003 22.418
DEMetro_Z 2 0.350 0.069 0.030 9.336
DEMetro_Z 3 0.868 0.059 0.025 31.823
DEMetro_Z 5 1.664 0.050 0.019 85.833
DEMetro_Z 8 5.284 0.043 0.010 518.211
DEMetro_Z 15 7.661 0.038 0.007 1090.155
DEMetro_Z 30 9.271 0.034 0.003 2683.139
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 8.361 3.19e-09 51.989
HMC 3 7.844 1.17e-08 43.389
HMC 5 8.688 1.42e-09 48.008
HMC 8 9.769 1.11e-10 74.063
HMC 15 9.088 5.45e-10 61.346
HMC 30 8.447 2.61e-09 80.880
SMC 2 -0.451 0.653 -0.109
SMC 3 -1.021 0.312 -0.229
SMC 5 -1.230 0.224 -0.275
SMC 8 -1.102 0.275 -0.277
SMC 15 -0.802 0.426 -0.184
SMC 30 1.556 0.126 0.458
Metro 2 6.315 6.44e-07 15.972
Metro 3 5.989 1.53e-06 11.496
Metro 5 7.241 4.98e-08 12.768
Metro 8 6.809 1.67e-07 16.398
Metro 15 8.537 1.76e-09 15.086
Metro 30 5.686 3.71e-06 20.241
DEMetro_Z 2 4.441 0.000117 9.782
DEMetro_Z 3 6.109 1.17e-06 31.276
DEMetro_Z 5 13.959 1.96e-14 55.160
DEMetro_Z 8 31.146 7e-24 165.944
DEMetro_Z 15 65.303 3.54e-33 221.365
DEMetro_Z 30 73.202 1.62e-34 408.479
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 4.484 0.000106 0.819
DEMetro_Z_vs_SMC 1 6.148 1.06e-06 1.122
DEMetro_Z_vs_SMC 2 13.988 2.01e-14 2.554
DEMetro_Z_vs_SMC 3 31.358 6.32e-24 5.725
DEMetro_Z_vs_SMC 4 65.605 4.36e-33 11.978
DEMetro_Z_vs_SMC 5 72.564 2.38e-34 13.248
HMC_vs_Metro 0 5.196 1.47e-05 0.949
HMC_vs_Metro 1 5.189 1.5e-05 0.947
HMC_vs_Metro 2 5.722 3.43e-06 1.045
HMC_vs_Metro 3 6.746 2.11e-07 1.232
HMC_vs_Metro 4 6.404 5.29e-07 1.169
HMC_vs_Metro 5 5.581 5.05e-06 1.019
Metro_vs_DEMetro_Z 0 1.919 0.0649 0.350
Metro_vs_DEMetro_Z 1 -3.765 0.000755 -0.687
Metro_vs_DEMetro_Z 2 -10.906 8.91e-12 -1.991
Metro_vs_DEMetro_Z 3 -24.884 4.09e-21 -4.543
Metro_vs_DEMetro_Z 4 -68.057 1.52e-33 -12.425
Metro_vs_DEMetro_Z 5 -58.090 1.45e-31 -10.606
HMC_vs_SMC 0 8.358 3.26e-09 1.526
HMC_vs_SMC 1 7.914 9.96e-09 1.445
HMC_vs_SMC 2 8.760 1.22e-09 1.599
HMC_vs_SMC 3 9.770 1.12e-10 1.784
HMC_vs_SMC 4 9.013 6.61e-10 1.645
HMC_vs_SMC 5 8.422 2.79e-09 1.538
Metro_vs_SMC 0 6.250 8.04e-07 1.141
Metro_vs_SMC 1 6.097 1.22e-06 1.113
Metro_vs_SMC 2 7.287 5.02e-08 1.330
Metro_vs_SMC 3 6.939 1.26e-07 1.267
Metro_vs_SMC 4 8.736 1.29e-09 1.595
Metro_vs_SMC 5 5.495 6.42e-06 1.003
HMC_vs_DEMetro_Z 0 6.487 4.22e-07 1.184
HMC_vs_DEMetro_Z 1 1.721 0.0958 0.314
HMC_vs_DEMetro_Z 2 -1.119 0.272 -0.204
HMC_vs_DEMetro_Z 3 -10.159 4.61e-11 -1.855
HMC_vs_DEMetro_Z 4 -20.124 1.39e-18 -3.674
HMC_vs_DEMetro_Z 5 -27.483 2.57e-22 -5.018
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.366 0.013 0.007 51.989
HMC 3 0.348 0.014 0.008 43.389
HMC 5 0.333 0.014 0.007 48.008
HMC 8 0.352 0.014 0.005 74.063
HMC 15 0.263 0.014 0.004 61.346
HMC 30 0.199 0.014 0.002 80.880
SMC 2 0.012 0.013 0.007 -0.109
SMC 3 0.012 0.014 0.008 -0.229
SMC 5 0.012 0.014 0.007 -0.275
SMC 8 0.013 0.014 0.005 -0.277
SMC 15 0.014 0.014 0.004 -0.184
SMC 30 0.015 0.014 0.002 0.458
Metro 2 0.122 0.013 0.007 15.972
Metro 3 0.102 0.014 0.008 11.496
Metro 5 0.099 0.014 0.007 12.768
Metro 8 0.089 0.014 0.005 16.398
Metro 15 0.075 0.014 0.004 15.086
Metro 30 0.060 0.014 0.002 20.241
DEMetro_Z 2 0.079 0.013 0.007 9.782
DEMetro_Z 3 0.254 0.014 0.008 31.276
DEMetro_Z 5 0.380 0.014 0.007 55.160
DEMetro_Z 8 0.771 0.014 0.005 165.944
DEMetro_Z 15 0.910 0.014 0.004 221.365
DEMetro_Z 30 0.947 0.014 0.002 408.479
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Mode Transitions (scatter)
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
Forest & Ridge Plots
Pooled
2 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
8 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
15 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
30 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
8 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
15 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
30 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2
3
5
8
15
30
Chain
2
3
5
8
15
30

two_attr_mm

▼

Varying_Mode_Distance_with_high_Dimension (Mixture, mm, 30 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 -6.986 3.5e-09 -1.673
HMC 4 -0.376 0.709 -0.131
HMC 6 5.947 1.72e-06 11.545
HMC 8 6.506 3.97e-07 36.222
HMC 10 4.791 4.52e-05 29.689
HMC 12 5.652 4.14e-06 38.971
SMC 0 1.363 0.178 0.377
SMC 4 1.672 0.0998 0.430
SMC 6 0.774 0.443 0.265
SMC 8 1.689 0.097 0.523
SMC 10 -0.468 0.641 -0.119
SMC 12 0.868 0.39 0.279
Metro 0 15.884 1.28e-19 6.394
Metro 4 13.874 1.43e-17 5.516
Metro 6 7.334 3.24e-08 8.306
Metro 8 7.187 6.35e-08 26.744
Metro 10 6.829 1.67e-07 35.289
Metro 12 5.947 1.83e-06 37.425
DEMetro_Z 0 33.756 7.88e-25 2716.720
DEMetro_Z 4 40.746 3.74e-27 2061.767
DEMetro_Z 6 40.112 5.85e-27 1898.382
DEMetro_Z 8 41.062 3e-27 1245.866
DEMetro_Z 10 51.607 4.27e-30 774.966
DEMetro_Z 12 41.324 2.48e-27 665.002
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -33.769 7.79e-25 -6.165
HMC_vs_DEMetro_Z 1 -40.706 3.85e-27 -7.432
HMC_vs_DEMetro_Z 2 -39.532 8.88e-27 -7.218
HMC_vs_DEMetro_Z 3 -40.347 4.96e-27 -7.366
HMC_vs_DEMetro_Z 4 -44.144 3.81e-28 -8.059
HMC_vs_DEMetro_Z 5 -41.041 3.05e-27 -7.493
Metro_vs_SMC 0 16.488 2.86e-16 3.010
Metro_vs_SMC 1 12.641 2.53e-13 2.308
Metro_vs_SMC 2 7.222 5.96e-08 1.319
Metro_vs_SMC 3 7.108 8.05e-08 1.298
Metro_vs_SMC 4 6.924 1.31e-07 1.264
Metro_vs_SMC 5 5.930 1.93e-06 1.083
Metro_vs_DEMetro_Z 0 -33.646 8.64e-25 -6.143
Metro_vs_DEMetro_Z 1 -40.696 3.88e-27 -7.430
Metro_vs_DEMetro_Z 2 -39.794 7.35e-27 -7.265
Metro_vs_DEMetro_Z 3 -39.809 7.28e-27 -7.268
Metro_vs_DEMetro_Z 4 -44.023 4.12e-28 -8.037
Metro_vs_DEMetro_Z 5 -39.785 7.4e-27 -7.264
HMC_vs_Metro 0 -22.194 9.6e-20 -4.052
HMC_vs_Metro 1 -13.729 3.22e-14 -2.507
HMC_vs_Metro 2 1.382 0.177 0.252
HMC_vs_Metro 3 1.396 0.173 0.255
HMC_vs_Metro 4 -0.933 0.359 -0.170
HMC_vs_Metro 5 0.407 0.687 0.074
HMC_vs_SMC 0 -9.670 1.41e-10 -1.765
HMC_vs_SMC 1 -1.714 0.0971 -0.313
HMC_vs_SMC 2 5.764 3.05e-06 1.052
HMC_vs_SMC 3 6.390 5.49e-07 1.167
HMC_vs_SMC 4 4.847 3.88e-05 0.885
HMC_vs_SMC 5 5.633 4.38e-06 1.028
DEMetro_Z_vs_SMC 0 33.751 7.91e-25 6.162
DEMetro_Z_vs_SMC 1 40.713 3.84e-27 7.433
DEMetro_Z_vs_SMC 2 40.021 6.25e-27 7.307
DEMetro_Z_vs_SMC 3 41.162 2.81e-27 7.515
DEMetro_Z_vs_SMC 4 51.529 4.53e-30 9.408
DEMetro_Z_vs_SMC 5 41.403 2.37e-27 7.559
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.018 0.022 0.002 -1.673
HMC 4 0.023 0.023 0.003 -0.131
HMC 6 0.065 0.025 0.003 11.545
HMC 8 0.213 0.026 0.005 36.222
HMC 10 0.270 0.029 0.008 29.689
HMC 12 0.408 0.031 0.010 38.971
SMC 0 0.023 0.022 0.002 0.377
SMC 4 0.025 0.023 0.003 0.430
SMC 6 0.026 0.025 0.003 0.265
SMC 8 0.029 0.026 0.005 0.523
SMC 10 0.028 0.029 0.008 -0.119
SMC 12 0.034 0.031 0.010 0.279
Metro 0 0.037 0.022 0.002 6.394
Metro 4 0.041 0.023 0.003 5.516
Metro 6 0.054 0.025 0.003 8.306
Metro 8 0.164 0.026 0.005 26.744
Metro 10 0.315 0.029 0.008 35.289
Metro 12 0.393 0.031 0.010 37.425
DEMetro_Z 0 6.531 0.022 0.002 2716.720
DEMetro_Z 4 6.740 0.023 0.003 2061.767
DEMetro_Z 6 6.623 0.025 0.003 1898.382
DEMetro_Z 8 6.469 0.026 0.005 1245.866
DEMetro_Z 10 6.314 0.029 0.008 774.966
DEMetro_Z 12 6.465 0.031 0.010 665.002
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 9.943 6.58e-14 2.917
HMC 4 4.433 4.58e-05 1.017
HMC 6 4.016 0.000223 1.532
HMC 8 4.084 0.000317 20.418
HMC 10 3.746 0.000792 59.976
HMC 12 4.233 0.000212 106.223
SMC 0 2.929 0.0049 0.832
SMC 4 4.308 8e-05 1.491
SMC 6 2.366 0.0219 0.798
SMC 8 2.113 0.039 0.593
SMC 10 2.398 0.0213 1.092
SMC 12 3.863 0.000371 1.550
Metro 0 16.403 8.54e-23 4.865
Metro 4 13.326 3.19e-19 3.622
Metro 6 6.805 6.83e-09 1.901
Metro 8 4.270 0.000188 11.440
Metro 10 5.002 2.52e-05 61.092
Metro 12 4.146 0.000269 95.038
DEMetro_Z 0 36.992 5.87e-26 42378.668
DEMetro_Z 4 37.271 4.75e-26 25311.282
DEMetro_Z 6 46.109 1.09e-28 13873.444
DEMetro_Z 8 40.318 5.06e-27 9812.353
DEMetro_Z 10 29.819 2.61e-23 12268.492
DEMetro_Z 12 32.340 2.65e-24 11072.193
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 7.274 5.2e-08 1.328
HMC_vs_SMC 1 -1.294 0.206 -0.236
HMC_vs_SMC 2 1.948 0.0612 0.356
HMC_vs_SMC 3 4.031 0.000368 0.736
HMC_vs_SMC 4 3.669 0.000976 0.670
HMC_vs_SMC 5 4.156 0.000262 0.759
Metro_vs_DEMetro_Z 0 -36.987 5.9e-26 -6.753
Metro_vs_DEMetro_Z 1 -37.265 4.77e-26 -6.804
Metro_vs_DEMetro_Z 2 -46.099 1.1e-28 -8.417
Metro_vs_DEMetro_Z 3 -40.156 5.68e-27 -7.332
Metro_vs_DEMetro_Z 4 -29.491 3.56e-23 -5.384
Metro_vs_DEMetro_Z 5 -31.569 5.23e-24 -5.764
HMC_vs_Metro 0 -5.498 6.37e-06 -1.004
HMC_vs_Metro 1 -11.672 1.77e-12 -2.131
HMC_vs_Metro 2 -1.043 0.306 -0.190
HMC_vs_Metro 3 1.566 0.128 0.286
HMC_vs_Metro 4 -0.070 0.945 -0.013
HMC_vs_Metro 5 1.073 0.292 0.196
HMC_vs_DEMetro_Z 0 -36.989 5.89e-26 -6.753
HMC_vs_DEMetro_Z 1 -37.269 4.75e-26 -6.804
HMC_vs_DEMetro_Z 2 -46.091 1.11e-28 -8.415
HMC_vs_DEMetro_Z 3 -40.080 6e-27 -7.318
HMC_vs_DEMetro_Z 4 -29.403 3.87e-23 -5.368
HMC_vs_DEMetro_Z 5 -31.674 4.76e-24 -5.783
Metro_vs_SMC 0 11.236 4.41e-12 2.051
Metro_vs_SMC 1 6.876 1.49e-07 1.255
Metro_vs_SMC 2 3.167 0.00361 0.578
Metro_vs_SMC 3 4.086 0.000316 0.746
Metro_vs_SMC 4 4.951 2.9e-05 0.904
Metro_vs_SMC 5 4.059 0.00034 0.741
DEMetro_Z_vs_SMC 0 36.991 5.88e-26 6.754
DEMetro_Z_vs_SMC 1 37.268 4.75e-26 6.804
DEMetro_Z_vs_SMC 2 46.102 1.1e-28 8.417
DEMetro_Z_vs_SMC 3 40.316 5.07e-27 7.361
DEMetro_Z_vs_SMC 4 29.817 2.61e-23 5.444
DEMetro_Z_vs_SMC 5 32.339 2.65e-24 5.904
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.043 0.032 0.004 2.917
HMC 4 0.043 0.036 0.007 1.017
HMC 6 0.060 0.041 0.013 1.532
HMC 8 0.386 0.045 0.017 20.418
HMC 10 0.833 0.046 0.013 59.976
HMC 12 1.662 0.044 0.015 106.223
SMC 0 0.035 0.032 0.004 0.832
SMC 4 0.046 0.036 0.007 1.491
SMC 6 0.051 0.041 0.013 0.798
SMC 8 0.055 0.045 0.017 0.593
SMC 10 0.060 0.046 0.013 1.092
SMC 12 0.067 0.044 0.015 1.550
Metro 0 0.051 0.032 0.004 4.865
Metro 4 0.060 0.036 0.007 3.622
Metro 6 0.065 0.041 0.013 1.901
Metro 8 0.236 0.045 0.017 11.440
Metro 10 0.848 0.046 0.013 61.092
Metro 12 1.491 0.044 0.015 95.038
DEMetro_Z 0 173.169 0.032 0.004 42378.668
DEMetro_Z 4 166.466 0.036 0.007 25311.282
DEMetro_Z 6 175.050 0.041 0.013 13873.444
DEMetro_Z 8 164.046 0.045 0.017 9812.353
DEMetro_Z 10 161.048 0.046 0.013 12268.492
DEMetro_Z 12 168.699 0.044 0.015 11072.193
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 -0.443 0.659 -0.101
HMC 4 2.330 0.0241 0.823
HMC 6 6.094 1.16e-06 12.761
HMC 8 6.358 5.96e-07 45.618
HMC 10 4.840 3.95e-05 39.048
HMC 12 5.722 3.42e-06 47.817
SMC 0 2.688 0.00943 0.769
SMC 4 2.988 0.00411 0.795
SMC 6 2.167 0.0349 0.709
SMC 8 2.113 0.0396 0.708
SMC 10 0.247 0.806 0.064
SMC 12 1.276 0.208 0.425
Metro 0 16.607 2.41e-19 7.722
Metro 4 16.255 5.38e-19 7.594
Metro 6 7.305 3.81e-08 9.675
Metro 8 6.988 1.09e-07 34.286
Metro 10 6.750 2.07e-07 45.083
Metro 12 5.992 1.62e-06 45.791
DEMetro_Z 0 63.569 1.08e-32 6844.797
DEMetro_Z 4 68.720 1.14e-33 5718.278
DEMetro_Z 6 65.446 4.67e-33 4521.960
DEMetro_Z 8 73.407 1.7e-34 3204.066
DEMetro_Z 10 62.858 1.49e-32 1940.523
DEMetro_Z 12 61.128 3.32e-32 1573.881
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -63.451 1.14e-32 -11.585
Metro_vs_DEMetro_Z 1 -68.625 1.19e-33 -12.529
Metro_vs_DEMetro_Z 2 -65.018 5.65e-33 -11.871
Metro_vs_DEMetro_Z 3 -71.765 3.28e-34 -13.102
Metro_vs_DEMetro_Z 4 -58.669 1.09e-31 -10.711
Metro_vs_DEMetro_Z 5 -57.594 1.85e-31 -10.515
DEMetro_Z_vs_SMC 0 63.522 1.11e-32 11.597
DEMetro_Z_vs_SMC 1 68.697 1.16e-33 12.542
DEMetro_Z_vs_SMC 2 65.430 4.71e-33 11.946
DEMetro_Z_vs_SMC 3 73.531 1.63e-34 13.425
DEMetro_Z_vs_SMC 4 62.839 1.51e-32 11.473
DEMetro_Z_vs_SMC 5 61.083 3.41e-32 11.152
HMC_vs_DEMetro_Z 0 -63.539 1.1e-32 -11.601
HMC_vs_DEMetro_Z 1 -68.642 1.18e-33 -12.532
HMC_vs_DEMetro_Z 2 -64.710 6.48e-33 -11.814
HMC_vs_DEMetro_Z 3 -70.046 6.6e-34 -12.789
HMC_vs_DEMetro_Z 4 -55.858 4.47e-31 -10.198
HMC_vs_DEMetro_Z 5 -61.428 2.9e-32 -11.215
HMC_vs_Metro 0 -17.886 3.31e-17 -3.266
HMC_vs_Metro 1 -14.943 3.71e-15 -2.728
HMC_vs_Metro 2 1.170 0.252 0.214
HMC_vs_Metro 3 1.288 0.208 0.235
HMC_vs_Metro 4 -0.768 0.449 -0.140
HMC_vs_Metro 5 0.430 0.67 0.079
HMC_vs_SMC 0 -4.343 0.000157 -0.793
HMC_vs_SMC 1 0.077 0.939 0.014
HMC_vs_SMC 2 5.719 3.45e-06 1.044
HMC_vs_SMC 3 6.249 8.06e-07 1.141
HMC_vs_SMC 4 4.854 3.8e-05 0.886
HMC_vs_SMC 5 5.685 3.79e-06 1.038
Metro_vs_SMC 0 16.493 2.84e-16 3.011
Metro_vs_SMC 1 13.771 2.98e-14 2.514
Metro_vs_SMC 2 6.851 1.59e-07 1.251
Metro_vs_SMC 3 6.874 1.49e-07 1.255
Metro_vs_SMC 4 6.787 1.89e-07 1.239
Metro_vs_SMC 5 5.952 1.82e-06 1.087
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.028 0.029 0.001 -0.101
HMC 4 0.031 0.030 0.002 0.823
HMC 6 0.061 0.032 0.002 12.761
HMC 8 0.175 0.034 0.003 45.618
HMC 10 0.230 0.036 0.005 39.048
HMC 12 0.335 0.038 0.006 47.817
SMC 0 0.030 0.029 0.001 0.769
SMC 4 0.031 0.030 0.002 0.795
SMC 6 0.034 0.032 0.002 0.709
SMC 8 0.036 0.034 0.003 0.708
SMC 10 0.036 0.036 0.005 0.064
SMC 12 0.041 0.038 0.006 0.425
Metro 0 0.040 0.029 0.001 7.722
Metro 4 0.043 0.030 0.002 7.594
Metro 6 0.054 0.032 0.002 9.675
Metro 8 0.140 0.034 0.003 34.286
Metro 10 0.260 0.036 0.005 45.083
Metro 12 0.323 0.038 0.006 45.791
DEMetro_Z 0 10.261 0.029 0.001 6844.797
DEMetro_Z 4 10.143 0.030 0.002 5718.278
DEMetro_Z 6 10.228 0.032 0.002 4521.960
DEMetro_Z 8 9.968 0.034 0.003 3204.066
DEMetro_Z 10 9.686 0.036 0.005 1940.523
DEMetro_Z 12 9.816 0.038 0.006 1573.881
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 -1.909 0.062 -0.420
HMC 4 1.490 0.142 0.499
HMC 6 6.042 1.33e-06 12.294
HMC 8 6.374 5.69e-07 40.710
HMC 10 4.764 4.88e-05 34.451
HMC 12 5.603 4.74e-06 43.903
SMC 0 3.157 0.00253 0.835
SMC 4 3.303 0.00164 0.828
SMC 6 2.121 0.039 0.721
SMC 8 2.370 0.0215 0.738
SMC 10 0.231 0.818 0.060
SMC 12 1.269 0.21 0.427
Metro 0 16.248 3.3e-20 6.354
Metro 4 14.329 6.76e-18 5.858
Metro 6 7.730 1.15e-08 9.158
Metro 8 7.034 9.58e-08 29.655
Metro 10 6.726 2.2e-07 40.278
Metro 12 5.832 2.52e-06 42.680
DEMetro_Z 0 102.700 7.7e-39 405.945
DEMetro_Z 4 105.407 3.19e-39 351.379
DEMetro_Z 6 104.167 4.63e-39 359.313
DEMetro_Z 8 90.436 2.44e-37 265.789
DEMetro_Z 10 102.094 3.01e-39 187.793
DEMetro_Z 12 64.207 4.36e-33 160.511
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 100.983 1.7e-38 18.437
DEMetro_Z_vs_SMC 1 105.936 4.26e-39 19.341
DEMetro_Z_vs_SMC 2 101.463 1.48e-38 18.525
DEMetro_Z_vs_SMC 3 91.965 2.55e-37 16.790
DEMetro_Z_vs_SMC 4 100.604 1.9e-38 18.368
DEMetro_Z_vs_SMC 5 64.429 7.35e-33 11.763
HMC_vs_Metro 0 -20.372 9.96e-19 -3.719
HMC_vs_Metro 1 -12.770 1.97e-13 -2.332
HMC_vs_Metro 2 1.266 0.216 0.231
HMC_vs_Metro 3 1.441 0.16 0.263
HMC_vs_Metro 4 -0.836 0.41 -0.153
HMC_vs_Metro 5 0.278 0.783 0.051
Metro_vs_DEMetro_Z 0 -98.431 3.57e-38 -17.971
Metro_vs_DEMetro_Z 1 -105.716 4.53e-39 -19.301
Metro_vs_DEMetro_Z 2 -91.104 3.34e-37 -16.633
Metro_vs_DEMetro_Z 3 -42.951 8.33e-28 -7.842
Metro_vs_DEMetro_Z 4 -22.684 5.27e-20 -4.142
Metro_vs_DEMetro_Z 5 -16.842 1.63e-16 -3.075
HMC_vs_SMC 0 -6.480 4.31e-07 -1.183
HMC_vs_SMC 1 -1.060 0.298 -0.194
HMC_vs_SMC 2 5.653 4.14e-06 1.032
HMC_vs_SMC 3 6.231 8.47e-07 1.138
HMC_vs_SMC 4 4.778 4.7e-05 0.872
HMC_vs_SMC 5 5.560 5.36e-06 1.015
Metro_vs_SMC 0 15.968 6.62e-16 2.915
Metro_vs_SMC 1 12.221 5.81e-13 2.231
Metro_vs_SMC 2 7.411 3.64e-08 1.353
Metro_vs_SMC 3 6.909 1.36e-07 1.261
Metro_vs_SMC 4 6.779 1.93e-07 1.238
Metro_vs_SMC 5 5.792 2.82e-06 1.057
HMC_vs_DEMetro_Z 0 -100.832 1.78e-38 -18.409
HMC_vs_DEMetro_Z 1 -103.784 7.72e-39 -18.948
HMC_vs_DEMetro_Z 2 -86.464 1.51e-36 -15.786
HMC_vs_DEMetro_Z 3 -37.815 3.14e-26 -6.904
HMC_vs_DEMetro_Z 4 -22.327 8.15e-20 -4.076
HMC_vs_DEMetro_Z 5 -15.990 6.38e-16 -2.919
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.013 0.014 0.001 -0.420
HMC 4 0.015 0.014 0.002 0.499
HMC 6 0.033 0.014 0.002 12.294
HMC 8 0.099 0.014 0.002 40.710
HMC 10 0.118 0.014 0.003 34.451
HMC 12 0.167 0.014 0.003 43.903
SMC 0 0.015 0.014 0.001 0.835
SMC 4 0.015 0.014 0.002 0.828
SMC 6 0.015 0.014 0.002 0.721
SMC 8 0.015 0.014 0.002 0.738
SMC 10 0.014 0.014 0.003 0.060
SMC 12 0.015 0.014 0.003 0.427
Metro 0 0.023 0.014 0.001 6.354
Metro 4 0.023 0.014 0.002 5.858
Metro 6 0.028 0.014 0.002 9.158
Metro 8 0.076 0.014 0.002 29.655
Metro 10 0.135 0.014 0.003 40.278
Metro 12 0.163 0.014 0.003 42.680
DEMetro_Z 0 0.575 0.014 0.001 405.945
DEMetro_Z 4 0.577 0.014 0.002 351.379
DEMetro_Z 6 0.573 0.014 0.002 359.313
DEMetro_Z 8 0.573 0.014 0.002 265.789
DEMetro_Z 10 0.580 0.014 0.003 187.793
DEMetro_Z 12 0.574 0.014 0.003 160.511
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 -6.614 1.51e-08 -1.564
HMC 4 1.036 0.306 0.415
HMC 6 4.528 9.16e-05 10.174
HMC 8 8.829 1.02e-09 79.837
HMC 10 301.630 1.89e-78 109.318
HMC 12 272.613 3.58e-71 110.229
SMC 0 -0.281 0.78 -0.078
SMC 4 0.810 0.421 0.209
SMC 6 -0.246 0.807 -0.077
SMC 8 -0.128 0.899 -0.033
SMC 10 -1.406 0.166 -0.319
SMC 12 1.760 0.0843 0.556
Metro 0 13.730 9.27e-17 6.137
Metro 4 11.273 1.48e-13 5.797
Metro 6 5.857 2.15e-06 9.484
Metro 8 7.148 7.05e-08 27.490
Metro 10 8.180 5.05e-09 57.824
Metro 12 28.949 5e-23 105.026
DEMetro_Z 0 19.632 2.71e-18 4192.915
DEMetro_Z 4 23.277 2.59e-20 3401.720
DEMetro_Z 6 23.604 1.76e-20 3162.635
DEMetro_Z 8 22.480 6.75e-20 2204.379
DEMetro_Z 10 26.791 5.23e-22 1445.795
DEMetro_Z 12 27.692 2.07e-22 1102.424
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -19.641 2.68e-18 -3.586
HMC_vs_DEMetro_Z 1 -23.266 2.62e-20 -4.248
HMC_vs_DEMetro_Z 2 -23.481 2.04e-20 -4.287
HMC_vs_DEMetro_Z 3 -21.280 3.04e-19 -3.885
HMC_vs_DEMetro_Z 4 -24.804 4.47e-21 -4.529
HMC_vs_DEMetro_Z 5 -24.920 3.92e-21 -4.550
Metro_vs_SMC 0 15.299 2.02e-15 2.793
Metro_vs_SMC 1 10.816 1.08e-11 1.975
Metro_vs_SMC 2 6.162 1.02e-06 1.125
Metro_vs_SMC 3 7.174 6.75e-08 1.310
Metro_vs_SMC 4 8.206 4.77e-09 1.498
Metro_vs_SMC 5 28.919 6.16e-23 5.280
Metro_vs_DEMetro_Z 0 -19.610 2.8e-18 -3.580
Metro_vs_DEMetro_Z 1 -23.209 2.8e-20 -4.237
Metro_vs_DEMetro_Z 2 -23.659 1.65e-20 -4.320
Metro_vs_DEMetro_Z 3 -22.216 9.34e-20 -4.056
Metro_vs_DEMetro_Z 4 -25.739 1.6e-21 -4.699
Metro_vs_DEMetro_Z 5 -25.411 2.28e-21 -4.639
HMC_vs_Metro 0 -18.599 1.16e-17 -3.396
HMC_vs_Metro 1 -10.970 7.77e-12 -2.003
HMC_vs_Metro 2 0.246 0.808 0.045
HMC_vs_Metro 3 4.833 4.03e-05 0.882
HMC_vs_Metro 4 7.235 5.76e-08 1.321
HMC_vs_Metro 5 1.457 0.156 0.266
HMC_vs_SMC 0 -6.459 4.56e-07 -1.179
HMC_vs_SMC 1 0.530 0.6 0.097
HMC_vs_SMC 2 4.429 0.000124 0.809
HMC_vs_SMC 3 8.817 1.06e-09 1.610
HMC_vs_SMC 4 320.591 4.98e-53 58.532
HMC_vs_SMC 5 264.115 1.37e-50 48.221
DEMetro_Z_vs_SMC 0 19.633 2.71e-18 3.585
DEMetro_Z_vs_SMC 1 23.275 2.6e-20 4.249
DEMetro_Z_vs_SMC 2 23.611 1.75e-20 4.311
DEMetro_Z_vs_SMC 3 22.479 6.76e-20 4.104
DEMetro_Z_vs_SMC 4 26.793 5.22e-22 4.892
DEMetro_Z_vs_SMC 5 27.676 2.11e-22 5.053
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.018 0.022 0.002 -1.564
HMC 4 0.025 0.023 0.003 0.415
HMC 6 0.061 0.025 0.003 10.174
HMC 8 0.439 0.026 0.005 79.837
HMC 10 0.916 0.029 0.008 109.318
HMC 12 1.097 0.031 0.010 110.229
SMC 0 0.022 0.022 0.002 -0.078
SMC 4 0.024 0.023 0.003 0.209
SMC 6 0.025 0.025 0.003 -0.077
SMC 8 0.026 0.026 0.005 -0.033
SMC 10 0.026 0.029 0.008 -0.319
SMC 12 0.036 0.031 0.010 0.556
Metro 0 0.037 0.022 0.002 6.137
Metro 4 0.042 0.023 0.003 5.797
Metro 6 0.058 0.025 0.003 9.484
Metro 8 0.168 0.026 0.005 27.490
Metro 10 0.498 0.029 0.008 57.824
Metro 12 1.047 0.031 0.010 105.026
DEMetro_Z 0 10.067 0.022 0.002 4192.915
DEMetro_Z 4 11.105 0.023 0.003 3401.720
DEMetro_Z 6 11.017 0.025 0.003 3162.635
DEMetro_Z 8 11.425 0.026 0.005 2204.379
DEMetro_Z 10 11.755 0.029 0.008 1445.795
DEMetro_Z 12 10.698 0.031 0.010 1102.424
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 12.259 1.1e-17 3.319
HMC 4 6.219 7.2e-08 1.441
HMC 6 2.948 0.00536 1.363
HMC 8 6.607 3.05e-07 83.890
HMC 10 748.044 1.54e-83 344.374
HMC 12 939.064 7.39e-88 428.369
SMC 0 1.675 0.0993 0.403
SMC 4 -1.141 0.259 -0.257
SMC 6 0.084 0.933 0.021
SMC 8 -0.938 0.352 -0.235
SMC 10 1.079 0.286 0.351
SMC 12 2.315 0.0256 0.972
Metro 0 15.240 6.64e-20 5.414
Metro 4 8.970 1.17e-11 3.320
Metro 6 5.978 1.63e-07 1.699
Metro 8 3.498 0.00152 10.945
Metro 10 5.600 4.79e-06 139.606
Metro 12 22.826 4.41e-20 399.940
DEMetro_Z 0 17.535 5.61e-17 4605.416
DEMetro_Z 4 16.845 1.63e-16 3282.899
DEMetro_Z 6 14.818 4.6e-15 1674.091
DEMetro_Z 8 15.202 2.38e-15 1246.384
DEMetro_Z 10 16.238 4.27e-16 1613.106
DEMetro_Z 12 17.078 1.13e-16 1405.463
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 12.793 1.88e-13 2.336
HMC_vs_SMC 1 9.143 4.84e-10 1.669
HMC_vs_SMC 2 2.880 0.0074 0.526
HMC_vs_SMC 3 6.602 3.1e-07 1.205
HMC_vs_SMC 4 831.907 4.89e-65 151.885
HMC_vs_SMC 5 779.694 3.2e-64 142.352
Metro_vs_DEMetro_Z 0 -17.514 5.79e-17 -3.198
Metro_vs_DEMetro_Z 1 -16.821 1.69e-16 -3.071
Metro_vs_DEMetro_Z 2 -14.800 4.75e-15 -2.702
Metro_vs_DEMetro_Z 3 -15.106 2.8e-15 -2.758
Metro_vs_DEMetro_Z 4 -14.633 6.35e-15 -2.672
Metro_vs_DEMetro_Z 5 -11.758 1.48e-12 -2.147
HMC_vs_Metro 0 -5.684 3.81e-06 -1.038
HMC_vs_Metro 1 -5.644 4.25e-06 -1.030
HMC_vs_Metro 2 -0.710 0.483 -0.130
HMC_vs_Metro 3 5.368 9.11e-06 0.980
HMC_vs_Metro 4 8.200 4.85e-09 1.497
HMC_vs_Metro 5 1.602 0.12 0.292
HMC_vs_DEMetro_Z 0 -17.520 5.74e-17 -3.199
HMC_vs_DEMetro_Z 1 -16.840 1.64e-16 -3.074
HMC_vs_DEMetro_Z 2 -14.805 4.7e-15 -2.703
HMC_vs_DEMetro_Z 3 -14.102 1.63e-14 -2.575
HMC_vs_DEMetro_Z 4 -12.779 1.94e-13 -2.333
HMC_vs_DEMetro_Z 5 -11.871 1.18e-12 -2.167
Metro_vs_SMC 0 17.396 6.94e-17 3.176
Metro_vs_SMC 1 12.344 4.54e-13 2.254
Metro_vs_SMC 2 6.969 1.16e-07 1.272
Metro_vs_SMC 3 3.713 0.000868 0.678
Metro_vs_SMC 4 5.577 5.11e-06 1.018
Metro_vs_SMC 5 22.531 6.34e-20 4.114
DEMetro_Z_vs_SMC 0 17.531 5.64e-17 3.201
DEMetro_Z_vs_SMC 1 16.846 1.62e-16 3.076
DEMetro_Z_vs_SMC 2 14.810 4.66e-15 2.704
DEMetro_Z_vs_SMC 3 15.205 2.36e-15 2.776
DEMetro_Z_vs_SMC 4 16.241 4.25e-16 2.965
DEMetro_Z_vs_SMC 5 17.076 1.13e-16 3.118
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.045 0.032 0.004 3.319
HMC 4 0.046 0.036 0.007 1.441
HMC 6 0.058 0.041 0.013 1.363
HMC 8 1.447 0.045 0.017 83.890
HMC 10 4.565 0.046 0.013 344.374
HMC 12 6.569 0.044 0.015 428.369
SMC 0 0.033 0.032 0.004 0.403
SMC 4 0.034 0.036 0.007 -0.257
SMC 6 0.041 0.041 0.013 0.021
SMC 8 0.041 0.045 0.017 -0.235
SMC 10 0.051 0.046 0.013 0.351
SMC 12 0.058 0.044 0.015 0.972
Metro 0 0.054 0.032 0.004 5.414
Metro 4 0.058 0.036 0.007 3.320
Metro 6 0.063 0.041 0.013 1.699
Metro 8 0.228 0.045 0.017 10.945
Metro 10 1.878 0.046 0.013 139.606
Metro 12 6.136 0.044 0.015 399.940
DEMetro_Z 0 18.847 0.032 0.004 4605.416
DEMetro_Z 4 21.622 0.036 0.007 3282.899
DEMetro_Z 6 21.159 0.041 0.013 1674.091
DEMetro_Z 8 20.877 0.045 0.017 1246.384
DEMetro_Z 10 21.215 0.046 0.013 1613.106
DEMetro_Z 12 21.452 0.044 0.015 1405.463
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 0.370 0.713 0.079
HMC 4 3.407 0.00138 1.274
HMC 6 4.603 7.47e-05 11.445
HMC 8 8.624 1.69e-09 104.698
HMC 10 115.499 1.24e-41 142.538
HMC 12 113.785 1.54e-41 135.723
SMC 0 -0.146 0.885 -0.040
SMC 4 0.807 0.423 0.216
SMC 6 -0.007 0.994 -0.002
SMC 8 -0.065 0.948 -0.018
SMC 10 -1.428 0.159 -0.316
SMC 12 1.642 0.107 0.509
Metro 0 16.819 3.79e-20 7.135
Metro 4 12.959 6.87e-15 7.772
Metro 6 5.919 1.85e-06 10.924
Metro 8 6.719 2.23e-07 34.105
Metro 10 8.128 5.76e-09 73.104
Metro 12 27.023 3.74e-22 132.208
DEMetro_Z 0 20.728 6.21e-19 5642.196
DEMetro_Z 4 24.233 8.51e-21 5243.783
DEMetro_Z 6 26.110 1.07e-21 4050.163
DEMetro_Z 8 22.512 6.5e-20 3075.673
DEMetro_Z 10 27.157 3.58e-22 1960.126
DEMetro_Z 12 29.071 5.31e-23 1443.620
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -20.709 6.37e-19 -3.781
Metro_vs_DEMetro_Z 1 -24.176 9.09e-21 -4.414
Metro_vs_DEMetro_Z 2 -26.163 1.01e-21 -4.777
Metro_vs_DEMetro_Z 3 -22.272 8.72e-20 -4.066
Metro_vs_DEMetro_Z 4 -26.301 8.75e-22 -4.802
Metro_vs_DEMetro_Z 5 -26.774 5.33e-22 -4.888
DEMetro_Z_vs_SMC 0 20.725 6.24e-19 3.784
DEMetro_Z_vs_SMC 1 24.233 8.52e-21 4.424
DEMetro_Z_vs_SMC 2 26.119 1.06e-21 4.769
DEMetro_Z_vs_SMC 3 22.512 6.5e-20 4.110
DEMetro_Z_vs_SMC 4 27.163 3.56e-22 4.959
DEMetro_Z_vs_SMC 5 29.069 5.33e-23 5.307
HMC_vs_DEMetro_Z 0 -20.729 6.21e-19 -3.785
HMC_vs_DEMetro_Z 1 -24.222 8.62e-21 -4.422
HMC_vs_DEMetro_Z 2 -25.993 1.22e-21 -4.746
HMC_vs_DEMetro_Z 3 -21.397 2.61e-19 -3.906
HMC_vs_DEMetro_Z 4 -25.219 2.82e-21 -4.604
HMC_vs_DEMetro_Z 5 -26.223 9.51e-22 -4.788
HMC_vs_Metro 0 -18.407 1.54e-17 -3.361
HMC_vs_Metro 1 -11.754 1.5e-12 -2.146
HMC_vs_Metro 2 0.163 0.872 0.030
HMC_vs_Metro 3 4.922 3.15e-05 0.899
HMC_vs_Metro 4 7.366 4.09e-08 1.345
HMC_vs_Metro 5 0.723 0.475 0.132
HMC_vs_SMC 0 0.583 0.564 0.106
HMC_vs_SMC 1 2.719 0.0109 0.496
HMC_vs_SMC 2 4.492 0.000104 0.820
HMC_vs_SMC 3 8.606 1.77e-09 1.571
HMC_vs_SMC 4 119.802 1.21e-40 21.873
HMC_vs_SMC 5 113.120 6.39e-40 20.653
Metro_vs_SMC 0 18.591 1.18e-17 3.394
Metro_vs_SMC 1 12.447 3.71e-13 2.272
Metro_vs_SMC 2 6.150 1.06e-06 1.123
Metro_vs_SMC 3 6.738 2.15e-07 1.230
Metro_vs_SMC 4 8.153 5.46e-09 1.488
Metro_vs_SMC 5 27.006 4.19e-22 4.931
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.029 0.029 0.001 0.079
HMC 4 0.032 0.030 0.002 1.274
HMC 6 0.058 0.032 0.002 11.445
HMC 8 0.358 0.034 0.003 104.698
HMC 10 0.745 0.036 0.005 142.538
HMC 12 0.881 0.038 0.006 135.723
SMC 0 0.028 0.029 0.001 -0.040
SMC 4 0.030 0.030 0.002 0.216
SMC 6 0.032 0.032 0.002 -0.002
SMC 8 0.033 0.034 0.003 -0.018
SMC 10 0.035 0.036 0.005 -0.316
SMC 12 0.041 0.038 0.006 0.509
Metro 0 0.039 0.029 0.001 7.135
Metro 4 0.044 0.030 0.002 7.772
Metro 6 0.057 0.032 0.002 10.924
Metro 8 0.139 0.034 0.003 34.105
Metro 10 0.400 0.036 0.005 73.104
Metro 12 0.860 0.038 0.006 132.208
DEMetro_Z 0 8.463 0.029 0.001 5642.196
DEMetro_Z 4 9.304 0.030 0.002 5243.783
DEMetro_Z 6 9.164 0.032 0.002 4050.163
DEMetro_Z 8 9.570 0.034 0.003 3075.673
DEMetro_Z 10 9.783 0.036 0.005 1960.126
DEMetro_Z 12 9.007 0.038 0.006 1443.620
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 -1.164 0.25 -0.261
HMC 4 2.686 0.01 0.982
HMC 6 4.624 7.02e-05 10.965
HMC 8 8.726 1.31e-09 90.777
HMC 10 141.163 1.3e-45 128.604
HMC 12 148.294 1.01e-46 126.378
SMC 0 0.633 0.529 0.165
SMC 4 0.992 0.326 0.259
SMC 6 0.172 0.864 0.053
SMC 8 -0.349 0.728 -0.091
SMC 10 -0.934 0.355 -0.212
SMC 12 1.811 0.0758 0.561
Metro 0 13.728 6.87e-17 5.980
Metro 4 12.361 7.09e-15 6.111
Metro 6 6.086 1.14e-06 10.262
Metro 8 7.022 9.9e-08 30.401
Metro 10 7.944 9.18e-09 67.634
Metro 12 28.439 8.64e-23 120.605
DEMetro_Z 0 86.839 1.24e-36 657.813
DEMetro_Z 4 78.852 2e-35 576.318
DEMetro_Z 6 118.626 1.31e-40 579.008
DEMetro_Z 8 68.206 1.29e-33 438.999
DEMetro_Z 10 61.773 2.13e-32 311.241
DEMetro_Z 12 61.765 2.01e-32 264.209
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 86.939 1.29e-36 15.873
DEMetro_Z_vs_SMC 1 79.083 1.99e-35 14.439
DEMetro_Z_vs_SMC 2 118.347 1.73e-40 21.607
DEMetro_Z_vs_SMC 3 68.173 1.44e-33 12.447
DEMetro_Z_vs_SMC 4 61.861 2.37e-32 11.294
DEMetro_Z_vs_SMC 5 61.133 3.33e-32 11.161
HMC_vs_Metro 0 -16.280 3.99e-16 -2.972
HMC_vs_Metro 1 -10.659 1.52e-11 -1.946
HMC_vs_Metro 2 0.235 0.816 0.043
HMC_vs_Metro 3 4.877 3.57e-05 0.890
HMC_vs_Metro 4 7.241 5.66e-08 1.322
HMC_vs_Metro 5 1.318 0.198 0.241
Metro_vs_DEMetro_Z 0 -87.236 1.17e-36 -15.927
Metro_vs_DEMetro_Z 1 -76.438 5.32e-35 -13.956
Metro_vs_DEMetro_Z 2 -113.312 6.08e-40 -20.688
Metro_vs_DEMetro_Z 3 -58.453 1.21e-31 -10.672
Metro_vs_DEMetro_Z 4 -22.403 7.42e-20 -4.090
Metro_vs_DEMetro_Z 5 -22.485 6.71e-20 -4.105
HMC_vs_SMC 0 -2.265 0.0312 -0.413
HMC_vs_SMC 1 2.102 0.0444 0.384
HMC_vs_SMC 2 4.515 9.73e-05 0.824
HMC_vs_SMC 3 8.722 1.33e-09 1.592
HMC_vs_SMC 4 142.599 7.83e-43 26.035
HMC_vs_SMC 5 147.735 2.81e-43 26.973
Metro_vs_SMC 0 14.992 3.41e-15 2.737
Metro_vs_SMC 1 11.726 1.58e-12 2.141
Metro_vs_SMC 2 6.348 6.16e-07 1.159
Metro_vs_SMC 3 7.070 8.88e-08 1.291
Metro_vs_SMC 4 7.956 8.95e-09 1.453
Metro_vs_SMC 5 28.400 1.02e-22 5.185
HMC_vs_DEMetro_Z 0 -86.965 1.28e-36 -15.878
HMC_vs_DEMetro_Z 1 -79.576 1.66e-35 -14.529
HMC_vs_DEMetro_Z 2 -95.742 7.95e-38 -17.480
HMC_vs_DEMetro_Z 3 -29.515 3.47e-23 -5.389
HMC_vs_DEMetro_Z 4 -36.484 8.7e-26 -6.661
HMC_vs_DEMetro_Z 5 -32.062 3.38e-24 -5.854
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.013 0.014 0.001 -0.261
HMC 4 0.015 0.014 0.002 0.982
HMC 6 0.031 0.014 0.002 10.965
HMC 8 0.205 0.014 0.002 90.777
HMC 10 0.402 0.014 0.003 128.604
HMC 12 0.455 0.014 0.003 126.378
SMC 0 0.014 0.014 0.001 0.165
SMC 4 0.014 0.014 0.002 0.259
SMC 6 0.014 0.014 0.002 0.053
SMC 8 0.013 0.014 0.002 -0.091
SMC 10 0.013 0.014 0.003 -0.212
SMC 12 0.016 0.014 0.003 0.561
Metro 0 0.022 0.014 0.001 5.980
Metro 4 0.024 0.014 0.002 6.111
Metro 6 0.030 0.014 0.002 10.262
Metro 8 0.078 0.014 0.002 30.401
Metro 10 0.218 0.014 0.003 67.634
Metro 12 0.435 0.014 0.003 120.605
DEMetro_Z 0 0.923 0.014 0.001 657.813
DEMetro_Z 4 0.938 0.014 0.002 576.318
DEMetro_Z 6 0.915 0.014 0.002 579.008
DEMetro_Z 8 0.938 0.014 0.002 438.999
DEMetro_Z 10 0.952 0.014 0.003 311.241
DEMetro_Z 12 0.936 0.014 0.003 264.209
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Mode Transitions (scatter)
Forest & Ridge Plots
Pooled
0 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
4 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
6 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
8 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
12 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
0 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
4 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
6 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
8 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
12 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
0
4
6
8
10
12
Chain
0
4
6
8
10
12

Varying_Mode_Distance_with_high_Correlation (Mixture, mm, 30 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 1.568 0.123 0.523
HMC 4 2.150 0.0369 0.806
HMC 6 5.682 3.38e-06 7.823
HMC 8 7.097 7.92e-08 20.652
HMC 10 5.970 1.68e-06 18.449
HMC 12 5.286 1.13e-05 21.701
SMC 0 -0.950 0.346 -0.222
SMC 4 -0.541 0.591 -0.141
SMC 6 1.750 0.0872 0.683
SMC 8 0.040 0.968 0.011
SMC 10 -0.555 0.581 -0.132
SMC 12 -0.301 0.764 -0.078
Metro 0 5.536 4.7e-06 5.780
Metro 4 7.365 1.58e-08 4.799
Metro 6 5.417 6.57e-06 5.576
Metro 8 6.713 1.83e-07 8.215
Metro 10 9.396 1.53e-10 10.180
Metro 12 9.108 4.73e-10 21.980
DEMetro_Z 0 3.404 0.00136 1.207
DEMetro_Z 4 2.433 0.0191 0.945
DEMetro_Z 6 5.745 2.18e-06 4.453
DEMetro_Z 8 4.860 3.61e-05 10.340
DEMetro_Z 10 8.552 1.78e-09 17.778
DEMetro_Z 12 6.677 2.47e-07 24.053
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -1.627 0.115 -0.297
HMC_vs_DEMetro_Z 1 -0.306 0.762 -0.056
HMC_vs_DEMetro_Z 2 2.255 0.0319 0.412
HMC_vs_DEMetro_Z 3 2.789 0.00923 0.509
HMC_vs_DEMetro_Z 4 0.173 0.864 0.032
HMC_vs_DEMetro_Z 5 -0.554 0.584 -0.101
Metro_vs_SMC 0 6.021 1.51e-06 1.099
Metro_vs_SMC 1 7.054 9.28e-08 1.288
Metro_vs_SMC 2 4.563 8.53e-05 0.833
Metro_vs_SMC 3 6.661 2.65e-07 1.216
Metro_vs_SMC 4 9.069 5.78e-10 1.656
Metro_vs_SMC 5 9.013 6.6e-10 1.646
Metro_vs_DEMetro_Z 0 4.570 8.37e-05 0.834
Metro_vs_DEMetro_Z 1 5.864 2.32e-06 1.071
Metro_vs_DEMetro_Z 2 0.923 0.364 0.168
Metro_vs_DEMetro_Z 3 -0.896 0.378 -0.164
Metro_vs_DEMetro_Z 4 -3.153 0.00374 -0.576
Metro_vs_DEMetro_Z 5 -0.440 0.663 -0.080
HMC_vs_Metro 0 -4.942 2.98e-05 -0.902
HMC_vs_Metro 1 -5.812 2.67e-06 -1.061
HMC_vs_Metro 2 1.160 0.255 0.212
HMC_vs_Metro 3 3.785 0.000714 0.691
HMC_vs_Metro 4 2.373 0.0245 0.433
HMC_vs_Metro 5 -0.052 0.959 -0.009
HMC_vs_SMC 0 2.493 0.0186 0.455
HMC_vs_SMC 1 2.414 0.0223 0.441
HMC_vs_SMC 2 5.235 1.32e-05 0.956
HMC_vs_SMC 3 7.203 6.26e-08 1.315
HMC_vs_SMC 4 6.053 1.38e-06 1.105
HMC_vs_SMC 5 5.280 1.16e-05 0.964
DEMetro_Z_vs_SMC 0 4.044 0.000355 0.738
DEMetro_Z_vs_SMC 1 2.830 0.00836 0.517
DEMetro_Z_vs_SMC 2 4.527 9.41e-05 0.827
DEMetro_Z_vs_SMC 3 4.780 4.67e-05 0.873
DEMetro_Z_vs_SMC 4 8.617 1.72e-09 1.573
DEMetro_Z_vs_SMC 5 6.656 2.68e-07 1.215
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.032 0.023 0.016 0.523
HMC 4 0.032 0.022 0.013 0.806
HMC 6 0.106 0.020 0.011 7.823
HMC 8 0.347 0.026 0.016 20.652
HMC 10 0.393 0.026 0.020 18.449
HMC 12 0.418 0.030 0.018 21.701
SMC 0 0.020 0.023 0.016 -0.222
SMC 4 0.020 0.022 0.013 -0.141
SMC 6 0.027 0.020 0.011 0.683
SMC 8 0.026 0.026 0.016 0.011
SMC 10 0.024 0.026 0.020 -0.132
SMC 12 0.028 0.030 0.018 -0.078
Metro 0 0.114 0.023 0.016 5.780
Metro 4 0.083 0.022 0.013 4.799
Metro 6 0.082 0.020 0.011 5.576
Metro 8 0.154 0.026 0.016 8.215
Metro 10 0.229 0.026 0.020 10.180
Metro 12 0.423 0.030 0.018 21.980
DEMetro_Z 0 0.042 0.023 0.016 1.207
DEMetro_Z 4 0.034 0.022 0.013 0.945
DEMetro_Z 6 0.069 0.020 0.011 4.453
DEMetro_Z 8 0.187 0.026 0.016 10.340
DEMetro_Z 10 0.379 0.026 0.020 17.778
DEMetro_Z 12 0.461 0.030 0.018 24.053
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 2.156 0.0372 1.000
HMC 4 4.702 2.87e-05 2.010
HMC 6 2.732 0.0087 0.915
HMC 8 4.643 6.43e-05 6.967
HMC 10 4.251 0.000198 9.985
HMC 12 3.890 0.000532 9.991
SMC 0 -2.572 0.0129 -0.587
SMC 4 1.153 0.254 0.349
SMC 6 -0.748 0.457 -0.213
SMC 8 -0.390 0.698 -0.092
SMC 10 1.364 0.178 0.381
SMC 12 -1.022 0.311 -0.239
Metro 0 7.268 3.91e-08 8.366
Metro 4 6.431 1.78e-07 3.478
Metro 6 5.427 5.37e-06 4.030
Metro 8 7.190 2.52e-08 4.588
Metro 10 6.801 1.24e-07 6.452
Metro 12 6.782 1.65e-07 10.360
DEMetro_Z 0 3.734 0.000525 1.407
DEMetro_Z 4 4.031 0.000217 1.573
DEMetro_Z 6 4.563 4.38e-05 1.921
DEMetro_Z 8 2.527 0.017 3.316
DEMetro_Z 10 6.212 7.09e-07 6.881
DEMetro_Z 12 4.467 0.000108 9.383
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 3.400 0.00198 0.621
HMC_vs_SMC 1 3.877 0.000558 0.708
HMC_vs_SMC 2 3.515 0.00147 0.642
HMC_vs_SMC 3 4.617 7.35e-05 0.843
HMC_vs_SMC 4 4.124 0.000285 0.753
HMC_vs_SMC 5 4.024 0.000375 0.735
Metro_vs_DEMetro_Z 0 6.037 1.44e-06 1.102
Metro_vs_DEMetro_Z 1 3.314 0.00248 0.605
Metro_vs_DEMetro_Z 2 2.477 0.0193 0.452
Metro_vs_DEMetro_Z 3 0.840 0.408 0.153
Metro_vs_DEMetro_Z 4 -0.297 0.769 -0.054
Metro_vs_DEMetro_Z 5 0.360 0.722 0.066
HMC_vs_Metro 0 -5.770 3e-06 -1.053
HMC_vs_Metro 1 -2.512 0.0178 -0.459
HMC_vs_Metro 2 -4.567 8.44e-05 -0.834
HMC_vs_Metro 3 1.547 0.133 0.282
HMC_vs_Metro 4 1.344 0.189 0.245
HMC_vs_Metro 5 -0.121 0.905 -0.022
HMC_vs_DEMetro_Z 0 -0.726 0.473 -0.133
HMC_vs_DEMetro_Z 1 0.864 0.395 0.158
HMC_vs_DEMetro_Z 2 -1.983 0.0569 -0.362
HMC_vs_DEMetro_Z 3 1.684 0.103 0.307
HMC_vs_DEMetro_Z 4 1.265 0.216 0.231
HMC_vs_DEMetro_Z 5 0.191 0.85 0.035
Metro_vs_SMC 0 7.696 1.74e-08 1.405
Metro_vs_SMC 1 5.119 1.82e-05 0.935
Metro_vs_SMC 2 5.850 2.41e-06 1.068
Metro_vs_SMC 3 7.456 3.23e-08 1.361
Metro_vs_SMC 4 6.374 5.75e-07 1.164
Metro_vs_SMC 5 6.888 1.44e-07 1.258
DEMetro_Z_vs_SMC 0 5.394 8.49e-06 0.985
DEMetro_Z_vs_SMC 1 3.390 0.00203 0.619
DEMetro_Z_vs_SMC 2 5.163 1.61e-05 0.943
DEMetro_Z_vs_SMC 3 2.565 0.0158 0.468
DEMetro_Z_vs_SMC 4 6.077 1.29e-06 1.110
DEMetro_Z_vs_SMC 5 4.615 7.39e-05 0.843
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.044 0.028 0.016 1.000
HMC 4 0.064 0.029 0.017 2.010
HMC 6 0.064 0.044 0.022 0.915
HMC 8 0.249 0.047 0.029 6.967
HMC 10 0.414 0.054 0.036 9.985
HMC 12 0.484 0.065 0.042 9.991
SMC 0 0.019 0.028 0.016 -0.587
SMC 4 0.035 0.029 0.017 0.349
SMC 6 0.039 0.044 0.022 -0.213
SMC 8 0.044 0.047 0.029 -0.092
SMC 10 0.067 0.054 0.036 0.381
SMC 12 0.055 0.065 0.042 -0.239
Metro 0 0.160 0.028 0.016 8.366
Metro 4 0.090 0.029 0.017 3.478
Metro 6 0.134 0.044 0.022 4.030
Metro 8 0.180 0.047 0.029 4.588
Metro 10 0.287 0.054 0.036 6.452
Metro 12 0.499 0.065 0.042 10.360
DEMetro_Z 0 0.050 0.028 0.016 1.407
DEMetro_Z 4 0.057 0.029 0.017 1.573
DEMetro_Z 6 0.087 0.044 0.022 1.921
DEMetro_Z 8 0.143 0.047 0.029 3.316
DEMetro_Z 10 0.302 0.054 0.036 6.881
DEMetro_Z 12 0.458 0.065 0.042 9.383
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 2.915 0.00532 0.979
HMC 4 4.854 1.79e-05 2.098
HMC 6 6.015 1.42e-06 11.279
HMC 8 6.979 1.1e-07 25.887
HMC 10 5.806 2.68e-06 25.060
HMC 12 5.433 7.56e-06 26.258
SMC 0 -1.588 0.118 -0.355
SMC 4 -0.553 0.583 -0.156
SMC 6 2.353 0.0235 1.026
SMC 8 -0.326 0.746 -0.083
SMC 10 0.157 0.875 0.040
SMC 12 -1.290 0.202 -0.320
Metro 0 7.325 3.39e-08 8.602
Metro 4 10.799 2.51e-12 7.985
Metro 6 8.180 3.45e-09 9.315
Metro 8 8.254 3.26e-09 11.583
Metro 10 11.065 4.3e-12 16.327
Metro 12 9.477 2.03e-10 27.583
DEMetro_Z 0 5.847 4.32e-07 2.054
DEMetro_Z 4 7.227 8.22e-09 3.162
DEMetro_Z 6 9.223 1.5e-10 7.376
DEMetro_Z 8 5.182 1.48e-05 12.971
DEMetro_Z 10 8.553 1.89e-09 25.263
DEMetro_Z 12 7.009 1.02e-07 29.212
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 5.825 2.58e-06 1.063
Metro_vs_DEMetro_Z 1 6.428 4.96e-07 1.174
Metro_vs_DEMetro_Z 2 1.424 0.165 0.260
Metro_vs_DEMetro_Z 3 -0.503 0.619 -0.092
Metro_vs_DEMetro_Z 4 -2.562 0.0159 -0.468
Metro_vs_DEMetro_Z 5 -0.299 0.767 -0.055
DEMetro_Z_vs_SMC 0 7.218 6.02e-08 1.318
DEMetro_Z_vs_SMC 1 6.925 1.31e-07 1.264
DEMetro_Z_vs_SMC 2 7.255 5.46e-08 1.325
DEMetro_Z_vs_SMC 3 5.167 1.6e-05 0.943
DEMetro_Z_vs_SMC 4 8.560 1.98e-09 1.563
DEMetro_Z_vs_SMC 5 7.087 8.49e-08 1.294
HMC_vs_DEMetro_Z 0 -2.531 0.017 -0.462
HMC_vs_DEMetro_Z 1 -1.867 0.0721 -0.341
HMC_vs_DEMetro_Z 2 1.985 0.0566 0.362
HMC_vs_DEMetro_Z 3 2.778 0.0095 0.507
HMC_vs_DEMetro_Z 4 -0.037 0.97 -0.007
HMC_vs_DEMetro_Z 5 -0.622 0.539 -0.114
HMC_vs_Metro 0 -6.373 5.76e-07 -1.164
HMC_vs_Metro 1 -8.568 1.94e-09 -1.564
HMC_vs_Metro 2 0.781 0.441 0.143
HMC_vs_Metro 3 3.503 0.00151 0.640
HMC_vs_Metro 4 1.795 0.083 0.328
HMC_vs_Metro 5 -0.210 0.835 -0.038
HMC_vs_SMC 0 4.180 0.000245 0.763
HMC_vs_SMC 1 4.644 6.81e-05 0.848
HMC_vs_SMC 2 5.515 6.07e-06 1.007
HMC_vs_SMC 3 7.043 9.54e-08 1.286
HMC_vs_SMC 4 5.827 2.56e-06 1.064
HMC_vs_SMC 5 5.509 6.17e-06 1.006
Metro_vs_SMC 0 7.830 1.23e-08 1.430
Metro_vs_SMC 1 10.082 5.49e-11 1.841
Metro_vs_SMC 2 6.878 1.48e-07 1.256
Metro_vs_SMC 3 8.241 4.37e-09 1.505
Metro_vs_SMC 4 10.662 1.51e-11 1.947
Metro_vs_SMC 5 9.476 2.21e-10 1.730
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.041 0.030 0.011 0.979
HMC 4 0.046 0.030 0.008 2.098
HMC 6 0.108 0.031 0.007 11.279
HMC 8 0.317 0.036 0.011 25.887
HMC 10 0.357 0.036 0.013 25.060
HMC 12 0.387 0.043 0.013 26.258
SMC 0 0.026 0.030 0.011 -0.355
SMC 4 0.029 0.030 0.008 -0.156
SMC 6 0.038 0.031 0.007 1.026
SMC 8 0.036 0.036 0.011 -0.083
SMC 10 0.037 0.036 0.013 0.040
SMC 12 0.039 0.043 0.013 -0.320
Metro 0 0.125 0.030 0.011 8.602
Metro 4 0.090 0.030 0.008 7.985
Metro 6 0.095 0.031 0.007 9.315
Metro 8 0.162 0.036 0.011 11.583
Metro 10 0.245 0.036 0.013 16.327
Metro 12 0.404 0.043 0.013 27.583
DEMetro_Z 0 0.053 0.030 0.011 2.054
DEMetro_Z 4 0.054 0.030 0.008 3.162
DEMetro_Z 6 0.081 0.031 0.007 7.376
DEMetro_Z 8 0.177 0.036 0.011 12.971
DEMetro_Z 10 0.359 0.036 0.013 25.263
DEMetro_Z 12 0.426 0.043 0.013 29.212
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 2.219 0.0307 0.677
HMC 4 4.999 8.87e-06 1.853
HMC 6 5.863 2.07e-06 8.687
HMC 8 7.136 7.21e-08 23.751
HMC 10 5.889 2.12e-06 21.933
HMC 12 5.161 1.61e-05 23.065
SMC 0 -1.302 0.199 -0.292
SMC 4 -0.481 0.633 -0.114
SMC 6 1.922 0.0607 0.681
SMC 8 -0.650 0.518 -0.158
SMC 10 -0.227 0.821 -0.054
SMC 12 -1.061 0.293 -0.261
Metro 0 7.392 2.52e-08 7.347
Metro 4 10.883 6.63e-13 6.095
Metro 6 9.669 3.34e-11 6.659
Metro 8 8.653 9.27e-10 8.893
Metro 10 12.644 9.15e-14 12.749
Metro 12 9.606 1.46e-10 23.589
DEMetro_Z 0 4.930 8.91e-06 1.579
DEMetro_Z 4 6.369 9.93e-08 2.514
DEMetro_Z 6 8.143 1.83e-09 5.440
DEMetro_Z 8 4.792 4.42e-05 12.093
DEMetro_Z 10 8.818 9.55e-10 21.070
DEMetro_Z 12 6.686 2.41e-07 25.739
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 6.174 9.91e-07 1.127
DEMetro_Z_vs_SMC 1 6.746 2.1e-07 1.232
DEMetro_Z_vs_SMC 2 6.819 1.73e-07 1.245
DEMetro_Z_vs_SMC 3 4.824 4.14e-05 0.881
DEMetro_Z_vs_SMC 4 8.871 9.3e-10 1.620
DEMetro_Z_vs_SMC 5 6.757 2.05e-07 1.234
HMC_vs_Metro 0 -6.900 1.39e-07 -1.260
HMC_vs_Metro 1 -8.774 1.18e-09 -1.602
HMC_vs_Metro 2 1.058 0.299 0.193
HMC_vs_Metro 3 4.238 0.000209 0.774
HMC_vs_Metro 4 2.237 0.0331 0.408
HMC_vs_Metro 5 -0.092 0.927 -0.017
Metro_vs_DEMetro_Z 0 5.964 1.76e-06 1.089
Metro_vs_DEMetro_Z 1 5.860 2.34e-06 1.070
Metro_vs_DEMetro_Z 2 1.312 0.2 0.240
Metro_vs_DEMetro_Z 3 -1.227 0.23 -0.224
Metro_vs_DEMetro_Z 4 -3.178 0.00351 -0.580
Metro_vs_DEMetro_Z 5 -0.458 0.65 -0.084
HMC_vs_SMC 0 3.521 0.00144 0.643
HMC_vs_SMC 1 5.166 1.6e-05 0.943
HMC_vs_SMC 2 5.663 4.03e-06 1.034
HMC_vs_SMC 3 7.206 6.21e-08 1.316
HMC_vs_SMC 4 5.930 1.93e-06 1.083
HMC_vs_SMC 5 5.224 1.36e-05 0.954
Metro_vs_SMC 0 8.045 7.15e-09 1.469
Metro_vs_SMC 1 10.607 1.71e-11 1.937
Metro_vs_SMC 2 8.162 5.33e-09 1.490
Metro_vs_SMC 3 8.759 1.22e-09 1.599
Metro_vs_SMC 4 12.202 6.04e-13 2.228
Metro_vs_SMC 5 9.579 1.74e-10 1.749
HMC_vs_DEMetro_Z 0 -2.363 0.0251 -0.431
HMC_vs_DEMetro_Z 1 -1.457 0.156 -0.266
HMC_vs_DEMetro_Z 2 2.020 0.0527 0.369
HMC_vs_DEMetro_Z 3 2.642 0.0132 0.482
HMC_vs_DEMetro_Z 4 0.188 0.852 0.034
HMC_vs_DEMetro_Z 5 -0.575 0.57 -0.105
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.022 0.016 0.008 0.677
HMC 4 0.024 0.014 0.005 1.853
HMC 6 0.053 0.014 0.005 8.687
HMC 8 0.150 0.014 0.006 23.751
HMC 10 0.154 0.013 0.006 21.933
HMC 12 0.152 0.014 0.006 23.065
SMC 0 0.014 0.016 0.008 -0.292
SMC 4 0.014 0.014 0.005 -0.114
SMC 6 0.017 0.014 0.005 0.681
SMC 8 0.013 0.014 0.006 -0.158
SMC 10 0.012 0.013 0.006 -0.054
SMC 12 0.012 0.014 0.006 -0.261
Metro 0 0.072 0.016 0.008 7.347
Metro 4 0.045 0.014 0.005 6.095
Metro 6 0.044 0.014 0.005 6.659
Metro 8 0.065 0.014 0.006 8.893
Metro 10 0.095 0.013 0.006 12.749
Metro 12 0.155 0.014 0.006 23.589
DEMetro_Z 0 0.028 0.016 0.008 1.579
DEMetro_Z 4 0.027 0.014 0.005 2.514
DEMetro_Z 6 0.039 0.014 0.005 5.440
DEMetro_Z 8 0.084 0.014 0.006 12.093
DEMetro_Z 10 0.149 0.013 0.006 21.070
DEMetro_Z 12 0.168 0.014 0.006 25.739
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 4.172 0.000116 1.340
HMC 4 2.535 0.0145 0.877
HMC 6 7.441 2.15e-08 7.195
HMC 8 9.013 6.2e-10 27.748
HMC 10 25.140 1.83e-21 51.048
HMC 12 140.313 3.49e-52 72.497
SMC 0 -1.147 0.256 -0.261
SMC 4 0.485 0.63 0.133
SMC 6 0.365 0.717 0.110
SMC 8 -0.546 0.588 -0.154
SMC 10 0.214 0.831 0.046
SMC 12 0.504 0.616 0.129
Metro 0 5.113 1.41e-05 4.122
Metro 4 5.297 7.82e-06 3.900
Metro 6 5.861 1.83e-06 5.874
Metro 8 6.304 5.45e-07 6.938
Metro 10 8.995 3.97e-10 9.396
Metro 12 8.637 1.55e-09 27.314
DEMetro_Z 0 1.233 0.223 0.429
DEMetro_Z 4 3.112 0.00342 1.404
DEMetro_Z 6 5.197 9.65e-06 3.401
DEMetro_Z 8 3.540 0.00136 8.732
DEMetro_Z 10 5.113 1.84e-05 22.534
DEMetro_Z 12 9.018 6.4e-10 51.072
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 2.249 0.0322 0.411
HMC_vs_DEMetro_Z 1 -0.955 0.348 -0.174
HMC_vs_DEMetro_Z 2 3.275 0.00274 0.598
HMC_vs_DEMetro_Z 3 4.939 3.01e-05 0.902
HMC_vs_DEMetro_Z 4 5.872 2.26e-06 1.072
HMC_vs_DEMetro_Z 5 3.678 0.000952 0.671
Metro_vs_SMC 0 5.645 4.24e-06 1.031
Metro_vs_SMC 1 4.947 2.94e-05 0.903
Metro_vs_SMC 2 5.615 4.6e-06 1.025
Metro_vs_SMC 3 6.241 8.25e-07 1.139
Metro_vs_SMC 4 8.935 7.96e-10 1.631
Metro_vs_SMC 5 8.662 1.54e-09 1.582
Metro_vs_DEMetro_Z 0 4.304 0.000174 0.786
Metro_vs_DEMetro_Z 1 3.006 0.00542 0.549
Metro_vs_DEMetro_Z 2 1.967 0.0589 0.359
Metro_vs_DEMetro_Z 3 -0.690 0.496 -0.126
Metro_vs_DEMetro_Z 4 -2.752 0.0101 -0.503
Metro_vs_DEMetro_Z 5 -4.293 0.00018 -0.784
HMC_vs_Metro 0 -3.470 0.00165 -0.634
HMC_vs_Metro 1 -4.218 0.00022 -0.770
HMC_vs_Metro 2 0.917 0.367 0.167
HMC_vs_Metro 3 6.689 2.45e-07 1.221
HMC_vs_Metro 4 20.033 1.57e-18 3.657
HMC_vs_Metro 5 13.931 2.22e-14 2.543
HMC_vs_SMC 0 5.682 3.82e-06 1.037
HMC_vs_SMC 1 1.781 0.0854 0.325
HMC_vs_SMC 2 7.355 4.21e-08 1.343
HMC_vs_SMC 3 9.081 5.62e-10 1.658
HMC_vs_SMC 4 24.998 3.6e-21 4.564
HMC_vs_SMC 5 142.504 7.98e-43 26.017
DEMetro_Z_vs_SMC 0 2.103 0.0443 0.384
DEMetro_Z_vs_SMC 1 2.877 0.00746 0.525
DEMetro_Z_vs_SMC 2 5.676 3.89e-06 1.036
DEMetro_Z_vs_SMC 3 3.706 0.000884 0.677
DEMetro_Z_vs_SMC 4 5.084 2.01e-05 0.928
DEMetro_Z_vs_SMC 5 8.981 7.12e-10 1.640
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.044 0.023 0.016 1.340
HMC 4 0.033 0.022 0.013 0.877
HMC 6 0.100 0.020 0.011 7.195
HMC 8 0.457 0.026 0.016 27.748
HMC 10 1.040 0.026 0.020 51.048
HMC 12 1.328 0.030 0.018 72.497
SMC 0 0.019 0.023 0.016 -0.261
SMC 4 0.023 0.022 0.013 0.133
SMC 6 0.021 0.020 0.011 0.110
SMC 8 0.024 0.026 0.016 -0.154
SMC 10 0.027 0.026 0.020 0.046
SMC 12 0.032 0.030 0.018 0.129
Metro 0 0.088 0.023 0.016 4.122
Metro 4 0.072 0.022 0.013 3.900
Metro 6 0.085 0.020 0.011 5.874
Metro 8 0.134 0.026 0.016 6.938
Metro 10 0.213 0.026 0.020 9.396
Metro 12 0.519 0.030 0.018 27.314
DEMetro_Z 0 0.030 0.023 0.016 0.429
DEMetro_Z 4 0.040 0.022 0.013 1.404
DEMetro_Z 6 0.057 0.020 0.011 3.401
DEMetro_Z 8 0.162 0.026 0.016 8.732
DEMetro_Z 10 0.474 0.026 0.020 22.534
DEMetro_Z 12 0.944 0.030 0.018 51.072
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 2.148 0.038 1.002
HMC 4 4.729 2.82e-05 2.141
HMC 6 3.881 0.000366 1.654
HMC 8 5.894 2.01e-06 12.406
HMC 10 21.423 1.61e-19 43.355
HMC 12 202.607 2.3e-82 57.462
SMC 0 -0.718 0.476 -0.179
SMC 4 1.164 0.25 0.377
SMC 6 -0.902 0.371 -0.251
SMC 8 0.803 0.425 0.225
SMC 10 -0.380 0.706 -0.097
SMC 12 -0.311 0.757 -0.071
Metro 0 4.993 2.14e-05 4.696
Metro 4 5.051 1.34e-05 2.927
Metro 6 4.158 0.000214 2.961
Metro 8 5.975 1.14e-06 4.764
Metro 10 7.451 1.68e-08 5.882
Metro 12 6.247 7.58e-07 12.927
DEMetro_Z 0 3.131 0.00334 1.541
DEMetro_Z 4 4.840 2.19e-05 2.394
DEMetro_Z 6 4.600 4.26e-05 2.101
DEMetro_Z 8 2.722 0.0107 3.670
DEMetro_Z 10 4.626 7.1e-05 17.411
DEMetro_Z 12 8.129 5.66e-09 39.436
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 2.658 0.0126 0.485
HMC_vs_SMC 1 5.065 2.12e-05 0.925
HMC_vs_SMC 2 4.943 2.97e-05 0.902
HMC_vs_SMC 3 5.891 2.15e-06 1.076
HMC_vs_SMC 4 21.820 1.53e-19 3.984
HMC_vs_SMC 5 196.745 6.98e-47 35.921
Metro_vs_DEMetro_Z 0 3.015 0.0053 0.550
Metro_vs_DEMetro_Z 1 0.757 0.455 0.138
Metro_vs_DEMetro_Z 2 1.072 0.292 0.196
Metro_vs_DEMetro_Z 3 0.725 0.474 0.132
Metro_vs_DEMetro_Z 4 -2.891 0.00721 -0.528
Metro_vs_DEMetro_Z 5 -5.784 2.89e-06 -1.056
HMC_vs_Metro 0 -3.342 0.0023 -0.610
HMC_vs_Metro 1 -1.179 0.248 -0.215
HMC_vs_Metro 2 -1.715 0.097 -0.313
HMC_vs_Metro 3 3.552 0.00133 0.649
HMC_vs_Metro 4 19.677 2.55e-18 3.592
HMC_vs_Metro 5 21.952 1.3e-19 4.008
HMC_vs_DEMetro_Z 0 -0.804 0.428 -0.147
HMC_vs_DEMetro_Z 1 -0.367 0.716 -0.067
HMC_vs_DEMetro_Z 2 -0.748 0.46 -0.137
HMC_vs_DEMetro_Z 3 3.432 0.00182 0.627
HMC_vs_DEMetro_Z 4 5.797 2.78e-06 1.058
HMC_vs_DEMetro_Z 5 3.804 0.00068 0.694
Metro_vs_SMC 0 4.970 2.76e-05 0.907
Metro_vs_SMC 1 4.686 6.07e-05 0.856
Metro_vs_SMC 2 4.318 0.000168 0.788
Metro_vs_SMC 3 5.876 2.24e-06 1.073
Metro_vs_SMC 4 7.260 5.39e-08 1.326
Metro_vs_SMC 5 6.386 5.55e-07 1.166
DEMetro_Z_vs_SMC 0 3.287 0.00265 0.600
DEMetro_Z_vs_SMC 1 3.614 0.00113 0.660
DEMetro_Z_vs_SMC 2 5.124 1.8e-05 0.936
DEMetro_Z_vs_SMC 3 2.522 0.0174 0.461
DEMetro_Z_vs_SMC 4 4.634 7.01e-05 0.846
DEMetro_Z_vs_SMC 5 8.174 5.17e-09 1.492
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.044 0.028 0.016 1.002
HMC 4 0.067 0.029 0.017 2.141
HMC 6 0.081 0.044 0.022 1.654
HMC 8 0.406 0.047 0.029 12.406
HMC 10 1.618 0.054 0.036 43.355
HMC 12 2.476 0.065 0.042 57.462
SMC 0 0.025 0.028 0.016 -0.179
SMC 4 0.036 0.029 0.017 0.377
SMC 6 0.038 0.044 0.022 -0.251
SMC 8 0.054 0.047 0.029 0.225
SMC 10 0.050 0.054 0.036 -0.097
SMC 12 0.062 0.065 0.042 -0.071
Metro 0 0.102 0.028 0.016 4.696
Metro 4 0.080 0.029 0.017 2.927
Metro 6 0.110 0.044 0.022 2.961
Metro 8 0.185 0.047 0.029 4.764
Metro 10 0.266 0.054 0.036 5.882
Metro 12 0.607 0.065 0.042 12.927
DEMetro_Z 0 0.052 0.028 0.016 1.541
DEMetro_Z 4 0.071 0.029 0.017 2.394
DEMetro_Z 6 0.091 0.044 0.022 2.101
DEMetro_Z 8 0.153 0.047 0.029 3.670
DEMetro_Z 10 0.682 0.054 0.036 17.411
DEMetro_Z 12 1.720 0.065 0.042 39.436
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 4.485 4.4e-05 1.529
HMC 4 4.543 4.34e-05 1.793
HMC 6 7.683 1.39e-08 10.119
HMC 8 8.845 9.51e-10 34.358
HMC 10 24.013 8.67e-21 71.103
HMC 12 64.023 1.1e-33 87.862
SMC 0 -1.485 0.144 -0.327
SMC 4 0.619 0.539 0.181
SMC 6 0.409 0.685 0.136
SMC 8 -0.489 0.626 -0.131
SMC 10 0.443 0.659 0.103
SMC 12 -0.422 0.674 -0.105
Metro 0 7.338 2.5e-08 6.227
Metro 4 6.817 1.21e-07 6.670
Metro 6 8.418 1.91e-09 9.865
Metro 8 8.810 7.19e-10 10.529
Metro 10 10.388 1.81e-11 14.012
Metro 12 9.092 5.22e-10 33.475
DEMetro_Z 0 4.129 0.000146 1.456
DEMetro_Z 4 7.771 1.41e-09 3.385
DEMetro_Z 6 7.699 8.52e-09 6.129
DEMetro_Z 8 3.702 0.000887 12.405
DEMetro_Z 10 5.266 1.2e-05 32.599
DEMetro_Z 12 8.945 7.69e-10 63.349
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 5.519 6e-06 1.008
Metro_vs_DEMetro_Z 1 3.081 0.00448 0.563
Metro_vs_DEMetro_Z 2 2.567 0.0157 0.469
Metro_vs_DEMetro_Z 3 -0.542 0.592 -0.099
Metro_vs_DEMetro_Z 4 -2.780 0.00945 -0.508
Metro_vs_DEMetro_Z 5 -4.291 0.000181 -0.783
DEMetro_Z_vs_SMC 0 5.323 1.03e-05 0.972
DEMetro_Z_vs_SMC 1 6.962 1.18e-07 1.271
DEMetro_Z_vs_SMC 2 7.981 8.42e-09 1.457
DEMetro_Z_vs_SMC 3 3.807 0.000674 0.695
DEMetro_Z_vs_SMC 4 5.215 1.39e-05 0.952
DEMetro_Z_vs_SMC 5 8.949 7.69e-10 1.634
HMC_vs_DEMetro_Z 0 0.174 0.863 0.032
HMC_vs_DEMetro_Z 1 -2.665 0.0125 -0.487
HMC_vs_DEMetro_Z 2 2.546 0.0165 0.465
HMC_vs_DEMetro_Z 3 4.375 0.000143 0.799
HMC_vs_DEMetro_Z 4 5.409 8.15e-06 0.987
HMC_vs_DEMetro_Z 5 3.342 0.0023 0.610
HMC_vs_Metro 0 -5.569 5.23e-06 -1.017
HMC_vs_Metro 1 -5.222 1.37e-05 -0.953
HMC_vs_Metro 2 0.134 0.895 0.024
HMC_vs_Metro 3 6.158 1.03e-06 1.124
HMC_vs_Metro 4 19.587 2.89e-18 3.576
HMC_vs_Metro 5 15.547 1.33e-15 2.838
HMC_vs_SMC 0 6.569 3.39e-07 1.199
HMC_vs_SMC 1 3.416 0.0019 0.624
HMC_vs_SMC 2 7.727 1.61e-08 1.411
HMC_vs_SMC 3 8.908 8.49e-10 1.626
HMC_vs_SMC 4 24.115 9.74e-21 4.403
HMC_vs_SMC 5 66.007 3.66e-33 12.051
Metro_vs_SMC 0 7.829 1.24e-08 1.429
Metro_vs_SMC 1 6.282 7.37e-07 1.147
Metro_vs_SMC 2 8.025 7.52e-09 1.465
Metro_vs_SMC 3 8.673 1.5e-09 1.583
Metro_vs_SMC 4 10.336 3.1e-11 1.887
Metro_vs_SMC 5 9.118 5.14e-10 1.665
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.047 0.030 0.011 1.529
HMC 4 0.044 0.030 0.008 1.793
HMC 6 0.100 0.031 0.007 10.119
HMC 8 0.409 0.036 0.011 34.358
HMC 10 0.945 0.036 0.013 71.103
HMC 12 1.195 0.043 0.013 87.862
SMC 0 0.026 0.030 0.011 -0.327
SMC 4 0.031 0.030 0.008 0.181
SMC 6 0.032 0.031 0.007 0.136
SMC 8 0.035 0.036 0.011 -0.131
SMC 10 0.038 0.036 0.013 0.103
SMC 12 0.041 0.043 0.013 -0.105
Metro 0 0.099 0.030 0.011 6.227
Metro 4 0.080 0.030 0.008 6.670
Metro 6 0.098 0.031 0.007 9.865
Metro 8 0.151 0.036 0.011 10.529
Metro 10 0.216 0.036 0.013 14.012
Metro 12 0.482 0.043 0.013 33.475
DEMetro_Z 0 0.046 0.030 0.011 1.456
DEMetro_Z 4 0.056 0.030 0.008 3.385
DEMetro_Z 6 0.073 0.031 0.007 6.129
DEMetro_Z 8 0.171 0.036 0.011 12.405
DEMetro_Z 10 0.453 0.036 0.013 32.599
DEMetro_Z 12 0.873 0.043 0.013 63.349
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 3.087 0.00325 0.993
HMC 4 4.341 7.63e-05 1.587
HMC 6 7.146 5.15e-08 7.533
HMC 8 8.757 1.18e-09 33.214
HMC 10 24.583 4.15e-21 62.753
HMC 12 160.963 2.48e-55 79.780
SMC 0 -1.319 0.193 -0.299
SMC 4 0.303 0.763 0.084
SMC 6 -0.310 0.758 -0.088
SMC 8 -0.572 0.57 -0.142
SMC 10 0.550 0.584 0.127
SMC 12 -0.756 0.453 -0.175
Metro 0 7.359 1.83e-08 5.181
Metro 4 6.496 2.11e-07 4.412
Metro 6 7.781 7.76e-09 6.858
Metro 8 9.545 7.71e-11 8.260
Metro 10 10.428 1.38e-11 11.792
Metro 12 9.144 4.51e-10 27.909
DEMetro_Z 0 3.342 0.00161 1.164
DEMetro_Z 4 7.360 1.9e-09 2.530
DEMetro_Z 6 6.842 6.44e-08 4.177
DEMetro_Z 8 3.700 0.000889 10.623
DEMetro_Z 10 5.200 1.45e-05 27.998
DEMetro_Z 12 8.960 7.38e-10 55.514
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 4.620 7.29e-05 0.843
DEMetro_Z_vs_SMC 1 6.775 1.95e-07 1.237
DEMetro_Z_vs_SMC 2 7.229 5.85e-08 1.320
DEMetro_Z_vs_SMC 3 3.791 0.000703 0.692
DEMetro_Z_vs_SMC 4 5.152 1.66e-05 0.941
DEMetro_Z_vs_SMC 5 9.002 6.77e-10 1.644
HMC_vs_Metro 0 -5.934 1.91e-06 -1.083
HMC_vs_Metro 1 -4.123 0.000286 -0.753
HMC_vs_Metro 2 0.453 0.654 0.083
HMC_vs_Metro 3 6.730 2.2e-07 1.229
HMC_vs_Metro 4 20.699 6.46e-19 3.779
HMC_vs_Metro 5 16.956 1.37e-16 3.096
Metro_vs_DEMetro_Z 0 5.302 1.1e-05 0.968
Metro_vs_DEMetro_Z 1 2.648 0.013 0.483
Metro_vs_DEMetro_Z 2 2.498 0.0184 0.456
Metro_vs_DEMetro_Z 3 -0.795 0.433 -0.145
Metro_vs_DEMetro_Z 4 -2.802 0.00894 -0.512
Metro_vs_DEMetro_Z 5 -4.625 7.19e-05 -0.844
HMC_vs_SMC 0 5.022 2.38e-05 0.917
HMC_vs_SMC 1 3.836 0.000624 0.700
HMC_vs_SMC 2 7.452 3.27e-08 1.360
HMC_vs_SMC 3 8.839 1e-09 1.614
HMC_vs_SMC 4 24.600 5.61e-21 4.491
HMC_vs_SMC 5 175.861 1.8e-45 32.108
Metro_vs_SMC 0 7.942 9.28e-09 1.450
Metro_vs_SMC 1 5.998 1.6e-06 1.095
Metro_vs_SMC 2 8.109 6.08e-09 1.481
Metro_vs_SMC 3 9.544 1.88e-10 1.742
Metro_vs_SMC 4 10.436 2.48e-11 1.905
Metro_vs_SMC 5 9.274 3.54e-10 1.693
HMC_vs_DEMetro_Z 0 -0.425 0.674 -0.078
HMC_vs_DEMetro_Z 1 -2.062 0.0483 -0.376
HMC_vs_DEMetro_Z 2 2.680 0.012 0.489
HMC_vs_DEMetro_Z 3 4.685 6.09e-05 0.855
HMC_vs_DEMetro_Z 4 5.695 3.68e-06 1.040
HMC_vs_DEMetro_Z 5 3.901 0.000523 0.712
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.024 0.016 0.008 0.993
HMC 4 0.022 0.014 0.005 1.587
HMC 6 0.048 0.014 0.005 7.533
HMC 8 0.205 0.014 0.006 33.214
HMC 10 0.418 0.013 0.006 62.753
HMC 12 0.491 0.014 0.006 79.780
SMC 0 0.014 0.016 0.008 -0.299
SMC 4 0.015 0.014 0.005 0.084
SMC 6 0.013 0.014 0.005 -0.088
SMC 8 0.013 0.014 0.006 -0.142
SMC 10 0.013 0.013 0.006 0.127
SMC 12 0.013 0.014 0.006 -0.175
Metro 0 0.055 0.016 0.008 5.181
Metro 4 0.036 0.014 0.005 4.412
Metro 6 0.045 0.014 0.005 6.858
Metro 8 0.062 0.014 0.006 8.260
Metro 10 0.089 0.013 0.006 11.792
Metro 12 0.181 0.014 0.006 27.909
DEMetro_Z 0 0.025 0.016 0.008 1.164
DEMetro_Z 4 0.027 0.014 0.005 2.530
DEMetro_Z 6 0.033 0.014 0.005 4.177
DEMetro_Z 8 0.075 0.014 0.006 10.623
DEMetro_Z 10 0.193 0.013 0.006 27.998
DEMetro_Z 12 0.346 0.014 0.006 55.514
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Mode Transitions (scatter)
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Forest & Ridge Plots
Pooled
0 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
4 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
6 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
8 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
12 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
0 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
4 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
6 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
8 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
12 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
0
4
6
8
10
12
Chain
0
4
6
8
10
12

Varying_Mode_Distance_with_heavy_Tails (Mixture, mm, 30 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 1.309 0.196 0.369
HMC 4 2.758 0.00818 0.952
HMC 6 2.352 0.0233 0.950
HMC 8 5.365 4.25e-06 2.652
HMC 10 5.048 1.75e-05 4.257
HMC 12 6.347 3.09e-07 4.130
SMC 0 3.351 0.00149 1.044
SMC 4 3.398 0.00165 1.798
SMC 6 3.536 0.00113 1.910
SMC 8 3.976 0.000302 1.952
SMC 10 3.772 0.000643 2.762
SMC 12 3.930 0.000355 2.017
Metro 0 2.556 0.0147 1.241
Metro 4 2.730 0.0102 2.131
Metro 6 2.695 0.0104 1.294
Metro 8 3.196 0.00253 1.189
Metro 10 4.326 0.000104 2.070
Metro 12 4.938 8.59e-06 1.572
DEMetro_Z 0 5.316 5.84e-06 3.000
DEMetro_Z 4 5.470 4.05e-06 3.395
DEMetro_Z 6 4.180 0.000137 1.641
DEMetro_Z 8 4.581 6.79e-05 3.928
DEMetro_Z 10 5.740 2.67e-06 6.201
DEMetro_Z 12 7.000 4.97e-08 4.835
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -4.396 0.000135 -0.803
HMC_vs_DEMetro_Z 1 -3.834 0.000627 -0.700
HMC_vs_DEMetro_Z 2 -1.337 0.191 -0.244
HMC_vs_DEMetro_Z 3 -1.384 0.177 -0.253
HMC_vs_DEMetro_Z 4 -1.571 0.127 -0.287
HMC_vs_DEMetro_Z 5 -0.831 0.413 -0.152
Metro_vs_SMC 0 0.395 0.696 0.072
Metro_vs_SMC 1 0.387 0.702 0.071
Metro_vs_SMC 2 -0.891 0.38 -0.163
Metro_vs_SMC 3 -1.360 0.184 -0.248
Metro_vs_SMC 4 -0.745 0.462 -0.136
Metro_vs_SMC 5 -0.802 0.429 -0.147
Metro_vs_DEMetro_Z 0 -2.558 0.016 -0.467
Metro_vs_DEMetro_Z 1 -1.491 0.147 -0.272
Metro_vs_DEMetro_Z 2 -0.644 0.524 -0.118
Metro_vs_DEMetro_Z 3 -2.810 0.00878 -0.513
Metro_vs_DEMetro_Z 4 -3.709 0.000876 -0.677
Metro_vs_DEMetro_Z 5 -4.432 0.000122 -0.809
HMC_vs_Metro 0 -1.604 0.12 -0.293
HMC_vs_Metro 1 -1.678 0.104 -0.306
HMC_vs_Metro 2 -0.704 0.487 -0.129
HMC_vs_Metro 3 2.134 0.0415 0.390
HMC_vs_Metro 4 2.301 0.0287 0.420
HMC_vs_Metro 5 3.637 0.00106 0.664
HMC_vs_SMC 0 -2.082 0.0463 -0.380
HMC_vs_SMC 1 -1.476 0.151 -0.269
HMC_vs_SMC 2 -1.664 0.107 -0.304
HMC_vs_SMC 3 0.960 0.345 0.175
HMC_vs_SMC 4 1.477 0.151 0.270
HMC_vs_SMC 5 2.654 0.0128 0.484
DEMetro_Z_vs_SMC 0 3.485 0.00159 0.636
DEMetro_Z_vs_SMC 1 2.194 0.0364 0.401
DEMetro_Z_vs_SMC 2 -0.419 0.678 -0.077
DEMetro_Z_vs_SMC 3 1.983 0.0569 0.362
DEMetro_Z_vs_SMC 4 2.237 0.0332 0.408
DEMetro_Z_vs_SMC 5 3.596 0.00118 0.657
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.067 0.056 0.031 0.369
HMC 4 0.081 0.056 0.026 0.952
HMC 6 0.133 0.084 0.051 0.950
HMC 8 0.234 0.080 0.058 2.652
HMC 10 0.329 0.096 0.055 4.257
HMC 12 0.535 0.091 0.108 4.130
SMC 0 0.088 0.056 0.031 1.044
SMC 4 0.103 0.056 0.026 1.798
SMC 6 0.182 0.084 0.051 1.910
SMC 8 0.193 0.080 0.058 1.952
SMC 10 0.247 0.096 0.055 2.762
SMC 12 0.308 0.091 0.108 2.017
Metro 0 0.094 0.056 0.031 1.241
Metro 4 0.111 0.056 0.026 2.131
Metro 6 0.150 0.084 0.051 1.294
Metro 8 0.149 0.080 0.058 1.189
Metro 10 0.210 0.096 0.055 2.070
Metro 12 0.260 0.091 0.108 1.572
DEMetro_Z 0 0.149 0.056 0.031 3.000
DEMetro_Z 4 0.144 0.056 0.026 3.395
DEMetro_Z 6 0.168 0.084 0.051 1.641
DEMetro_Z 8 0.308 0.080 0.058 3.928
DEMetro_Z 10 0.435 0.096 0.055 6.201
DEMetro_Z 12 0.611 0.091 0.108 4.835
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 -1.293 0.206 -0.239
HMC 4 -1.207 0.236 -0.229
HMC 6 -1.460 0.154 -0.272
HMC 8 -0.548 0.586 -0.123
HMC 10 -0.913 0.365 -0.214
HMC 12 -0.981 0.335 -0.179
SMC 0 -0.898 0.376 -0.165
SMC 4 -0.267 0.791 -0.050
SMC 6 -1.631 0.114 -0.299
SMC 8 -0.813 0.421 -0.159
SMC 10 -1.725 0.0939 -0.325
SMC 12 -0.984 0.333 -0.180
Metro 0 -1.449 0.158 -0.265
Metro 4 -1.421 0.165 -0.264
Metro 6 -1.373 0.18 -0.254
Metro 8 -0.715 0.479 -0.141
Metro 10 -1.676 0.103 -0.316
Metro 12 -0.968 0.341 -0.177
DEMetro_Z 0 -1.155 0.257 -0.214
DEMetro_Z 4 -1.266 0.215 -0.235
DEMetro_Z 6 -1.483 0.149 -0.273
DEMetro_Z 8 -0.607 0.547 -0.122
DEMetro_Z 10 -1.390 0.174 -0.259
DEMetro_Z 12 -0.961 0.345 -0.175
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -1.959 0.0598 -0.358
HMC_vs_SMC 1 -2.939 0.00641 -0.537
HMC_vs_SMC 2 0.783 0.44 0.143
HMC_vs_SMC 3 0.348 0.73 0.064
HMC_vs_SMC 4 0.790 0.436 0.144
HMC_vs_SMC 5 0.186 0.854 0.034
Metro_vs_DEMetro_Z 0 -1.860 0.0731 -0.340
Metro_vs_DEMetro_Z 1 -1.576 0.126 -0.288
Metro_vs_DEMetro_Z 2 0.762 0.452 0.139
Metro_vs_DEMetro_Z 3 -0.466 0.645 -0.085
Metro_vs_DEMetro_Z 4 -1.510 0.142 -0.276
Metro_vs_DEMetro_Z 5 -0.791 0.435 -0.144
HMC_vs_Metro 0 0.925 0.363 0.169
HMC_vs_Metro 1 0.711 0.483 0.130
HMC_vs_Metro 2 -0.442 0.662 -0.081
HMC_vs_Metro 3 0.155 0.878 0.028
HMC_vs_Metro 4 0.820 0.419 0.150
HMC_vs_Metro 5 -1.329 0.194 -0.243
HMC_vs_DEMetro_Z 0 -0.631 0.533 -0.115
HMC_vs_DEMetro_Z 1 0.131 0.896 0.024
HMC_vs_DEMetro_Z 2 0.008 0.994 0.001
HMC_vs_DEMetro_Z 3 -0.006 0.995 -0.001
HMC_vs_DEMetro_Z 4 0.366 0.717 0.067
HMC_vs_DEMetro_Z 5 -2.908 0.00692 -0.531
Metro_vs_SMC 0 -4.134 0.000278 -0.755
Metro_vs_SMC 1 -3.909 0.000512 -0.714
Metro_vs_SMC 2 1.812 0.0804 0.331
Metro_vs_SMC 3 0.255 0.801 0.046
Metro_vs_SMC 4 0.161 0.874 0.029
Metro_vs_SMC 5 1.082 0.288 0.197
DEMetro_Z_vs_SMC 0 -1.754 0.09 -0.320
DEMetro_Z_vs_SMC 1 -3.258 0.00286 -0.595
DEMetro_Z_vs_SMC 2 1.646 0.111 0.300
DEMetro_Z_vs_SMC 3 0.660 0.515 0.120
DEMetro_Z_vs_SMC 4 1.152 0.259 0.210
DEMetro_Z_vs_SMC 5 1.686 0.103 0.308
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 4.678 12.635 33.274 -0.239
HMC 4 4.973 9.021 17.702 -0.229
HMC 6 5.422 15.222 35.975 -0.272
HMC 8 4.518 5.811 10.534 -0.123
HMC 10 5.039 7.441 11.232 -0.214
HMC 12 5.723 72.267 371.333 -0.179
SMC 0 7.140 12.635 33.274 -0.165
SMC 4 8.133 9.021 17.702 -0.050
SMC 6 4.463 15.222 35.975 -0.299
SMC 8 4.141 5.811 10.534 -0.159
SMC 10 3.790 7.441 11.232 -0.325
SMC 12 5.571 72.267 371.333 -0.180
Metro 0 3.806 12.635 33.274 -0.265
Metro 4 4.344 9.021 17.702 -0.264
Metro 6 6.084 15.222 35.975 -0.254
Metro 8 4.326 5.811 10.534 -0.141
Metro 10 3.894 7.441 11.232 -0.316
Metro 12 6.599 72.267 371.333 -0.177
DEMetro_Z 0 5.509 12.635 33.274 -0.214
DEMetro_Z 4 4.858 9.021 17.702 -0.235
DEMetro_Z 6 5.413 15.222 35.975 -0.273
DEMetro_Z 8 4.526 5.811 10.534 -0.122
DEMetro_Z 10 4.533 7.441 11.232 -0.259
DEMetro_Z 12 7.105 72.267 371.333 -0.175
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 2.275 0.0266 0.594
HMC 4 3.169 0.00277 1.230
HMC 6 3.361 0.0016 1.295
HMC 8 6.230 4.1e-07 3.862
HMC 10 5.645 3.08e-06 4.748
HMC 12 6.674 1.01e-07 3.970
SMC 0 9.304 1.46e-10 8.206
SMC 4 9.158 1.72e-10 7.230
SMC 6 7.747 3.04e-09 4.075
SMC 8 9.615 2.76e-11 5.964
SMC 10 9.123 1.2e-10 5.958
SMC 12 7.425 4.23e-09 3.224
Metro 0 4.788 1.61e-05 1.647
Metro 4 5.969 4.58e-07 2.533
Metro 6 4.904 1.85e-05 2.498
Metro 8 6.749 2.71e-08 2.651
Metro 10 5.650 1.79e-06 2.854
Metro 12 6.022 1.66e-07 1.864
DEMetro_Z 0 9.778 5.07e-13 3.411
DEMetro_Z 4 10.233 7.89e-14 3.436
DEMetro_Z 6 8.326 6.17e-11 2.850
DEMetro_Z 8 6.707 1.67e-07 6.713
DEMetro_Z 10 7.246 3.94e-08 7.688
DEMetro_Z 12 7.404 1.42e-08 4.842
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -4.569 8.38e-05 -0.834
Metro_vs_DEMetro_Z 1 -2.128 0.0419 -0.389
Metro_vs_DEMetro_Z 2 -0.614 0.544 -0.112
Metro_vs_DEMetro_Z 3 -3.603 0.00116 -0.658
Metro_vs_DEMetro_Z 4 -4.156 0.000261 -0.759
Metro_vs_DEMetro_Z 5 -4.334 0.00016 -0.791
DEMetro_Z_vs_SMC 0 -5.298 1.11e-05 -0.967
DEMetro_Z_vs_SMC 1 -4.549 8.86e-05 -0.831
DEMetro_Z_vs_SMC 2 -2.046 0.05 -0.373
DEMetro_Z_vs_SMC 3 0.615 0.543 0.112
DEMetro_Z_vs_SMC 4 1.248 0.222 0.228
DEMetro_Z_vs_SMC 5 2.200 0.0359 0.402
HMC_vs_DEMetro_Z 0 -8.076 6.61e-09 -1.475
HMC_vs_DEMetro_Z 1 -5.374 8.97e-06 -0.981
HMC_vs_DEMetro_Z 2 -4.007 0.000392 -0.732
HMC_vs_DEMetro_Z 3 -2.560 0.0159 -0.467
HMC_vs_DEMetro_Z 4 -2.457 0.0202 -0.449
HMC_vs_DEMetro_Z 5 -1.114 0.274 -0.203
HMC_vs_Metro 0 -3.141 0.00385 -0.574
HMC_vs_Metro 1 -2.634 0.0134 -0.481
HMC_vs_Metro 2 -2.422 0.0219 -0.442
HMC_vs_Metro 3 1.459 0.155 0.266
HMC_vs_Metro 4 2.040 0.0506 0.372
HMC_vs_Metro 5 3.315 0.00247 0.605
HMC_vs_SMC 0 -9.005 6.73e-10 -1.644
HMC_vs_SMC 1 -7.134 7.5e-08 -1.303
HMC_vs_SMC 2 -4.913 3.23e-05 -0.897
HMC_vs_SMC 3 -2.429 0.0216 -0.444
HMC_vs_SMC 4 -1.192 0.243 -0.218
HMC_vs_SMC 5 1.055 0.3 0.193
Metro_vs_SMC 0 -7.317 4.65e-08 -1.336
Metro_vs_SMC 1 -5.877 2.23e-06 -1.073
Metro_vs_SMC 2 -2.268 0.0309 -0.414
Metro_vs_SMC 3 -4.577 8.2e-05 -0.836
Metro_vs_SMC 4 -3.940 0.000471 -0.719
Metro_vs_SMC 5 -2.941 0.00636 -0.537
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.149 0.123 0.044 0.594
HMC 4 0.179 0.130 0.040 1.230
HMC 6 0.217 0.156 0.048 1.295
HMC 8 0.299 0.145 0.040 3.862
HMC 10 0.388 0.159 0.048 4.748
HMC 12 0.592 0.168 0.107 3.970
SMC 0 0.481 0.123 0.044 8.206
SMC 4 0.417 0.130 0.040 7.230
SMC 6 0.349 0.156 0.048 4.075
SMC 8 0.382 0.145 0.040 5.964
SMC 10 0.447 0.159 0.048 5.958
SMC 12 0.512 0.168 0.107 3.224
Metro 0 0.195 0.123 0.044 1.647
Metro 4 0.230 0.130 0.040 2.533
Metro 6 0.274 0.156 0.048 2.498
Metro 8 0.250 0.145 0.040 2.651
Metro 10 0.297 0.159 0.048 2.854
Metro 12 0.367 0.168 0.107 1.864
DEMetro_Z 0 0.272 0.123 0.044 3.411
DEMetro_Z 4 0.266 0.130 0.040 3.436
DEMetro_Z 6 0.291 0.156 0.048 2.850
DEMetro_Z 8 0.412 0.145 0.040 6.713
DEMetro_Z 10 0.530 0.159 0.048 7.688
DEMetro_Z 12 0.685 0.168 0.107 4.842
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 3.233 0.00208 0.966
HMC 4 4.833 2.75e-05 3.003
HMC 6 4.258 0.00015 2.613
HMC 8 5.729 2.24e-06 4.329
HMC 10 5.507 5.31e-06 6.415
HMC 12 7.303 4.45e-08 16.621
SMC 0 11.812 9.23e-13 18.868
SMC 4 10.447 1.61e-11 14.392
SMC 6 7.072 5.49e-08 6.264
SMC 8 6.921 5.92e-08 4.613
SMC 10 6.140 7.26e-07 5.065
SMC 12 5.665 3.68e-06 9.359
Metro 0 7.670 1.65e-09 3.212
Metro 4 6.152 8.05e-07 6.284
Metro 6 6.027 3.69e-07 2.532
Metro 8 4.785 2.06e-05 1.947
Metro 10 5.127 1.02e-05 2.841
Metro 12 6.960 7.64e-08 6.297
DEMetro_Z 0 7.593 1.19e-08 6.232
DEMetro_Z 4 9.555 5.87e-11 7.314
DEMetro_Z 6 6.849 4.82e-08 3.665
DEMetro_Z 8 5.262 1.08e-05 6.495
DEMetro_Z 10 6.555 2.99e-07 9.166
DEMetro_Z 12 7.127 7.25e-08 19.058
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 -6.558 3.49e-07 -1.197
DEMetro_Z_vs_SMC 1 -4.415 0.000128 -0.806
DEMetro_Z_vs_SMC 2 -2.522 0.0174 -0.461
DEMetro_Z_vs_SMC 3 1.340 0.191 0.245
DEMetro_Z_vs_SMC 4 2.207 0.0354 0.403
DEMetro_Z_vs_SMC 5 3.273 0.00275 0.598
HMC_vs_Metro 0 -5.050 2.21e-05 -0.922
HMC_vs_Metro 1 -3.672 0.000968 -0.670
HMC_vs_Metro 2 0.122 0.904 0.022
HMC_vs_Metro 3 2.441 0.021 0.446
HMC_vs_Metro 4 2.739 0.0104 0.500
HMC_vs_Metro 5 4.028 0.00037 0.735
Metro_vs_DEMetro_Z 0 -2.974 0.00587 -0.543
Metro_vs_DEMetro_Z 1 -0.757 0.455 -0.138
Metro_vs_DEMetro_Z 2 -1.647 0.11 -0.301
Metro_vs_DEMetro_Z 3 -3.375 0.00211 -0.616
Metro_vs_DEMetro_Z 4 -4.060 0.00034 -0.741
Metro_vs_DEMetro_Z 5 -4.397 0.000135 -0.803
HMC_vs_SMC 0 -11.627 1.94e-12 -2.123
HMC_vs_SMC 1 -7.445 3.32e-08 -1.359
HMC_vs_SMC 2 -3.914 0.000506 -0.715
HMC_vs_SMC 3 -0.263 0.795 -0.048
HMC_vs_SMC 4 0.996 0.328 0.182
HMC_vs_SMC 5 2.602 0.0144 0.475
Metro_vs_SMC 0 -10.018 6.33e-11 -1.829
Metro_vs_SMC 1 -4.832 4.05e-05 -0.882
Metro_vs_SMC 2 -4.178 0.000246 -0.763
Metro_vs_SMC 3 -3.610 0.00114 -0.659
Metro_vs_SMC 4 -2.073 0.0472 -0.378
Metro_vs_SMC 5 -1.555 0.131 -0.284
HMC_vs_DEMetro_Z 0 -6.200 9.21e-07 -1.132
HMC_vs_DEMetro_Z 1 -4.110 0.000297 -0.750
HMC_vs_DEMetro_Z 2 -1.382 0.178 -0.252
HMC_vs_DEMetro_Z 3 -1.572 0.127 -0.287
HMC_vs_DEMetro_Z 4 -1.747 0.0913 -0.319
HMC_vs_DEMetro_Z 5 -0.726 0.474 -0.133
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.019 0.015 0.004 0.966
HMC 4 0.022 0.012 0.003 3.003
HMC 6 0.029 0.014 0.006 2.613
HMC 8 0.041 0.013 0.006 4.329
HMC 10 0.051 0.012 0.006 6.415
HMC 12 0.069 0.010 0.004 16.621
SMC 0 0.096 0.015 0.004 18.868
SMC 4 0.058 0.012 0.003 14.392
SMC 6 0.050 0.014 0.006 6.264
SMC 8 0.043 0.013 0.006 4.613
SMC 10 0.043 0.012 0.006 5.065
SMC 12 0.043 0.010 0.004 9.359
Metro 0 0.029 0.015 0.004 3.212
Metro 4 0.032 0.012 0.003 6.284
Metro 6 0.029 0.014 0.006 2.532
Metro 8 0.026 0.013 0.006 1.947
Metro 10 0.029 0.012 0.006 2.841
Metro 12 0.032 0.010 0.004 6.297
DEMetro_Z 0 0.042 0.015 0.004 6.232
DEMetro_Z 4 0.036 0.012 0.003 7.314
DEMetro_Z 6 0.035 0.014 0.006 3.665
DEMetro_Z 8 0.055 0.013 0.006 6.495
DEMetro_Z 10 0.067 0.012 0.006 9.166
DEMetro_Z 12 0.078 0.010 0.004 19.058
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 1.791 0.0801 0.704
HMC 4 3.146 0.00316 1.483
HMC 6 3.472 0.00107 1.149
HMC 8 5.338 3.35e-06 2.163
HMC 10 4.226 0.000176 3.011
HMC 12 6.793 6.42e-08 3.837
SMC 0 1.577 0.121 0.490
SMC 4 3.236 0.00262 1.839
SMC 6 2.155 0.0368 0.870
SMC 8 4.025 0.000239 1.733
SMC 10 4.749 3.85e-05 3.396
SMC 12 6.436 8.93e-08 2.642
Metro 0 2.894 0.00665 1.979
Metro 4 3.468 0.00145 2.326
Metro 6 3.746 0.000607 1.925
Metro 8 4.147 0.000188 2.132
Metro 10 4.062 0.000256 2.321
Metro 12 3.842 0.000414 1.646
DEMetro_Z 0 3.908 0.000462 3.511
DEMetro_Z 4 5.110 1.48e-05 4.422
DEMetro_Z 6 4.649 3.75e-05 2.173
DEMetro_Z 8 3.716 0.000739 2.552
DEMetro_Z 10 5.380 5.99e-06 3.840
DEMetro_Z 12 6.243 4.29e-07 4.119
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -3.350 0.00225 -0.612
HMC_vs_DEMetro_Z 1 -2.744 0.0103 -0.501
HMC_vs_DEMetro_Z 2 -1.859 0.0732 -0.339
HMC_vs_DEMetro_Z 3 -0.503 0.619 -0.092
HMC_vs_DEMetro_Z 4 -0.862 0.396 -0.157
HMC_vs_DEMetro_Z 5 -0.356 0.725 -0.065
Metro_vs_SMC 0 2.424 0.0218 0.443
Metro_vs_SMC 1 0.757 0.455 0.138
Metro_vs_SMC 2 1.792 0.0835 0.327
Metro_vs_SMC 3 0.646 0.523 0.118
Metro_vs_SMC 4 -1.358 0.185 -0.248
Metro_vs_SMC 5 -1.819 0.0793 -0.332
Metro_vs_DEMetro_Z 0 -1.264 0.216 -0.231
Metro_vs_DEMetro_Z 1 -1.850 0.0746 -0.338
Metro_vs_DEMetro_Z 2 -0.417 0.68 -0.076
Metro_vs_DEMetro_Z 3 -0.508 0.615 -0.093
Metro_vs_DEMetro_Z 4 -1.720 0.0961 -0.314
Metro_vs_DEMetro_Z 5 -3.104 0.00423 -0.567
HMC_vs_Metro 0 -1.663 0.107 -0.304
HMC_vs_Metro 1 -0.967 0.341 -0.177
HMC_vs_Metro 2 -1.427 0.164 -0.261
HMC_vs_Metro 3 0.054 0.958 0.010
HMC_vs_Metro 4 0.762 0.452 0.139
HMC_vs_Metro 5 3.057 0.00477 0.558
HMC_vs_SMC 0 0.499 0.622 0.091
HMC_vs_SMC 1 -0.489 0.629 -0.089
HMC_vs_SMC 2 0.618 0.541 0.113
HMC_vs_SMC 3 0.816 0.421 0.149
HMC_vs_SMC 4 -0.381 0.706 -0.070
HMC_vs_SMC 5 1.613 0.118 0.294
DEMetro_Z_vs_SMC 0 3.258 0.00286 0.595
DEMetro_Z_vs_SMC 1 2.475 0.0194 0.452
DEMetro_Z_vs_SMC 2 2.508 0.018 0.458
DEMetro_Z_vs_SMC 3 1.267 0.215 0.231
DEMetro_Z_vs_SMC 4 0.409 0.686 0.075
DEMetro_Z_vs_SMC 5 1.859 0.0731 0.339
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.078 0.056 0.031 0.704
HMC 4 0.095 0.056 0.026 1.483
HMC 6 0.143 0.084 0.051 1.149
HMC 8 0.206 0.080 0.058 2.163
HMC 10 0.261 0.096 0.055 3.011
HMC 12 0.504 0.091 0.108 3.837
SMC 0 0.071 0.056 0.031 0.490
SMC 4 0.104 0.056 0.026 1.839
SMC 6 0.129 0.084 0.051 0.870
SMC 8 0.181 0.080 0.058 1.733
SMC 10 0.282 0.096 0.055 3.396
SMC 12 0.375 0.091 0.108 2.642
Metro 0 0.117 0.056 0.031 1.979
Metro 4 0.116 0.056 0.026 2.326
Metro 6 0.183 0.084 0.051 1.925
Metro 8 0.204 0.080 0.058 2.132
Metro 10 0.223 0.096 0.055 2.321
Metro 12 0.268 0.091 0.108 1.646
DEMetro_Z 0 0.164 0.056 0.031 3.511
DEMetro_Z 4 0.170 0.056 0.026 4.422
DEMetro_Z 6 0.195 0.084 0.051 2.173
DEMetro_Z 8 0.228 0.080 0.058 2.552
DEMetro_Z 10 0.306 0.096 0.055 3.840
DEMetro_Z 12 0.534 0.091 0.108 4.119
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 -0.601 0.55 -0.130
HMC 4 -0.835 0.408 -0.170
HMC 6 -0.945 0.351 -0.187
HMC 8 -0.817 0.419 -0.164
HMC 10 -1.167 0.25 -0.242
HMC 12 -0.968 0.341 -0.177
SMC 0 -1.339 0.191 -0.246
SMC 4 -1.178 0.248 -0.219
SMC 6 -1.778 0.0858 -0.326
SMC 8 -1.104 0.276 -0.217
SMC 10 -1.781 0.0839 -0.338
SMC 12 -0.982 0.334 -0.179
Metro 0 -1.101 0.279 -0.207
Metro 4 -1.518 0.139 -0.284
Metro 6 -1.300 0.203 -0.241
Metro 8 -0.367 0.715 -0.081
Metro 10 -1.201 0.238 -0.232
Metro 12 -0.923 0.364 -0.169
DEMetro_Z 0 -1.136 0.265 -0.211
DEMetro_Z 4 -1.464 0.154 -0.271
DEMetro_Z 6 -1.356 0.185 -0.250
DEMetro_Z 8 -0.401 0.691 -0.082
DEMetro_Z 10 -1.582 0.123 -0.297
DEMetro_Z 12 -0.961 0.345 -0.175
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 0.991 0.33 0.181
HMC_vs_SMC 1 0.524 0.604 0.096
HMC_vs_SMC 2 1.795 0.0831 0.328
HMC_vs_SMC 3 1.080 0.289 0.197
HMC_vs_SMC 4 0.897 0.377 0.164
HMC_vs_SMC 5 2.221 0.0344 0.405
Metro_vs_DEMetro_Z 0 0.092 0.928 0.017
Metro_vs_DEMetro_Z 1 -0.735 0.468 -0.134
Metro_vs_DEMetro_Z 2 0.298 0.768 0.054
Metro_vs_DEMetro_Z 3 0.011 0.992 0.002
Metro_vs_DEMetro_Z 4 1.091 0.284 0.199
Metro_vs_DEMetro_Z 5 0.835 0.411 0.152
HMC_vs_Metro 0 0.640 0.528 0.117
HMC_vs_Metro 1 1.408 0.17 0.257
HMC_vs_Metro 2 0.657 0.516 0.120
HMC_vs_Metro 3 -0.744 0.463 -0.136
HMC_vs_Metro 4 -0.090 0.929 -0.016
HMC_vs_Metro 5 -1.013 0.319 -0.185
HMC_vs_DEMetro_Z 0 0.686 0.498 0.125
HMC_vs_DEMetro_Z 1 1.232 0.228 0.225
HMC_vs_DEMetro_Z 2 0.772 0.446 0.141
HMC_vs_DEMetro_Z 3 -1.283 0.21 -0.234
HMC_vs_DEMetro_Z 4 0.615 0.543 0.112
HMC_vs_DEMetro_Z 5 -0.884 0.384 -0.161
Metro_vs_SMC 0 0.856 0.399 0.156
Metro_vs_SMC 1 -1.360 0.184 -0.248
Metro_vs_SMC 2 3.425 0.00186 0.625
Metro_vs_SMC 3 1.623 0.115 0.296
Metro_vs_SMC 4 1.779 0.0857 0.325
Metro_vs_SMC 5 1.336 0.192 0.244
DEMetro_Z_vs_SMC 0 1.020 0.316 0.186
DEMetro_Z_vs_SMC 1 -1.174 0.25 -0.214
DEMetro_Z_vs_SMC 2 4.219 0.00022 0.770
DEMetro_Z_vs_SMC 3 2.511 0.0179 0.458
DEMetro_Z_vs_SMC 4 0.836 0.41 0.153
DEMetro_Z_vs_SMC 5 3.097 0.00431 0.565
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 8.321 12.635 33.274 -0.130
HMC 4 6.020 9.021 17.702 -0.170
HMC 6 8.486 15.222 35.975 -0.187
HMC 8 4.085 5.811 10.534 -0.164
HMC 10 4.727 7.441 11.232 -0.242
HMC 12 6.639 72.267 371.333 -0.177
SMC 0 4.443 12.635 33.274 -0.246
SMC 4 5.137 9.021 17.702 -0.219
SMC 6 3.503 15.222 35.975 -0.326
SMC 8 3.521 5.811 10.534 -0.217
SMC 10 3.640 7.441 11.232 -0.338
SMC 12 5.689 72.267 371.333 -0.179
Metro 0 5.759 12.635 33.274 -0.207
Metro 4 4.000 9.021 17.702 -0.284
Metro 6 6.560 15.222 35.975 -0.241
Metro 8 4.958 5.811 10.534 -0.081
Metro 10 4.839 7.441 11.232 -0.232
Metro 12 9.634 72.267 371.333 -0.169
DEMetro_Z 0 5.609 12.635 33.274 -0.211
DEMetro_Z 4 4.227 9.021 17.702 -0.271
DEMetro_Z 6 6.244 15.222 35.975 -0.250
DEMetro_Z 8 4.948 5.811 10.534 -0.082
DEMetro_Z 10 4.101 7.441 11.232 -0.297
DEMetro_Z 12 7.136 72.267 371.333 -0.175
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 2.933 0.00538 1.198
HMC 4 3.713 0.000557 1.388
HMC 6 4.712 2.36e-05 1.776
HMC 8 5.847 1.14e-06 3.296
HMC 10 5.220 9.47e-06 3.647
HMC 12 6.805 5.48e-08 3.630
SMC 0 5.081 1.6e-05 4.366
SMC 4 5.767 1.77e-06 3.799
SMC 6 3.892 0.000352 1.645
SMC 8 6.805 5.83e-08 3.732
SMC 10 6.318 4e-07 4.757
SMC 12 6.841 1.86e-08 2.640
Metro 0 5.231 5.72e-06 2.373
Metro 4 4.941 1.11e-05 1.863
Metro 6 5.175 7.58e-06 2.523
Metro 8 5.622 2.5e-06 3.420
Metro 10 6.217 3.53e-07 3.413
Metro 12 3.956 0.000315 1.877
DEMetro_Z 0 7.338 8.92e-09 3.657
DEMetro_Z 4 7.264 1.43e-08 3.953
DEMetro_Z 6 9.507 2.36e-12 3.589
DEMetro_Z 8 5.439 5.8e-06 4.884
DEMetro_Z 10 7.968 3.26e-09 5.557
DEMetro_Z 12 7.044 3.43e-08 4.229
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -2.106 0.044 -0.384
Metro_vs_DEMetro_Z 1 -3.710 0.000873 -0.677
Metro_vs_DEMetro_Z 2 -2.103 0.0442 -0.384
Metro_vs_DEMetro_Z 3 -1.543 0.134 -0.282
Metro_vs_DEMetro_Z 4 -2.465 0.0198 -0.450
Metro_vs_DEMetro_Z 5 -3.095 0.00434 -0.565
DEMetro_Z_vs_SMC 0 -0.824 0.417 -0.150
DEMetro_Z_vs_SMC 1 0.169 0.867 0.031
DEMetro_Z_vs_SMC 2 4.568 8.41e-05 0.834
DEMetro_Z_vs_SMC 3 1.541 0.134 0.281
DEMetro_Z_vs_SMC 4 0.714 0.481 0.130
DEMetro_Z_vs_SMC 5 2.140 0.0409 0.391
HMC_vs_DEMetro_Z 0 -4.495 0.000103 -0.821
HMC_vs_DEMetro_Z 1 -4.060 0.00034 -0.741
HMC_vs_DEMetro_Z 2 -3.666 0.000983 -0.669
HMC_vs_DEMetro_Z 3 -1.505 0.143 -0.275
HMC_vs_DEMetro_Z 4 -2.171 0.0383 -0.396
HMC_vs_DEMetro_Z 5 -0.831 0.413 -0.152
HMC_vs_Metro 0 -2.116 0.0431 -0.386
HMC_vs_Metro 1 -0.965 0.343 -0.176
HMC_vs_Metro 2 -1.217 0.233 -0.222
HMC_vs_Metro 3 -0.158 0.875 -0.029
HMC_vs_Metro 4 0.283 0.779 0.052
HMC_vs_Metro 5 2.466 0.0198 0.450
HMC_vs_SMC 0 -3.350 0.00226 -0.612
HMC_vs_SMC 1 -3.032 0.00508 -0.554
HMC_vs_SMC 2 0.251 0.804 0.046
HMC_vs_SMC 3 -0.589 0.56 -0.108
HMC_vs_SMC 4 -1.135 0.266 -0.207
HMC_vs_SMC 5 1.452 0.157 0.265
Metro_vs_SMC 0 -2.116 0.043 -0.386
Metro_vs_SMC 1 -2.675 0.0121 -0.488
Metro_vs_SMC 2 1.590 0.123 0.290
Metro_vs_SMC 3 -0.467 0.644 -0.085
Metro_vs_SMC 4 -1.590 0.123 -0.290
Metro_vs_SMC 5 -1.322 0.197 -0.241
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.175 0.123 0.044 1.198
HMC 4 0.185 0.130 0.040 1.388
HMC 6 0.240 0.156 0.048 1.776
HMC 8 0.276 0.145 0.040 3.296
HMC 10 0.335 0.159 0.048 3.647
HMC 12 0.556 0.168 0.107 3.630
SMC 0 0.313 0.123 0.044 4.366
SMC 4 0.281 0.130 0.040 3.799
SMC 6 0.234 0.156 0.048 1.645
SMC 8 0.293 0.145 0.040 3.732
SMC 10 0.389 0.159 0.048 4.757
SMC 12 0.450 0.168 0.107 2.640
Metro 0 0.226 0.123 0.044 2.373
Metro 4 0.204 0.130 0.040 1.863
Metro 6 0.275 0.156 0.048 2.523
Metro 8 0.281 0.145 0.040 3.420
Metro 10 0.324 0.159 0.048 3.413
Metro 12 0.369 0.168 0.107 1.877
DEMetro_Z 0 0.282 0.123 0.044 3.657
DEMetro_Z 4 0.287 0.130 0.040 3.953
DEMetro_Z 6 0.326 0.156 0.048 3.589
DEMetro_Z 8 0.339 0.145 0.040 4.884
DEMetro_Z 10 0.427 0.159 0.048 5.557
DEMetro_Z 12 0.620 0.168 0.107 4.229
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 2.775 0.00907 2.072
HMC 4 5.489 3.32e-06 3.010
HMC 6 4.321 0.00012 2.468
HMC 8 5.573 3.03e-06 3.528
HMC 10 4.783 3.96e-05 4.644
HMC 12 7.235 5.26e-08 15.288
SMC 0 6.839 1.45e-07 11.651
SMC 4 7.655 1.45e-08 9.538
SMC 6 4.600 5.68e-05 3.007
SMC 8 5.340 6.29e-06 3.495
SMC 10 5.575 4.03e-06 5.259
SMC 12 7.631 1.65e-08 10.772
Metro 0 8.397 4.26e-10 4.362
Metro 4 8.392 6.2e-10 4.846
Metro 6 5.334 3.21e-06 2.097
Metro 8 4.628 4.4e-05 2.391
Metro 10 6.135 3.77e-07 3.044
Metro 12 6.444 2.66e-07 4.664
DEMetro_Z 0 9.820 1.02e-11 5.438
DEMetro_Z 4 7.443 2.1e-08 7.067
DEMetro_Z 6 8.308 4.91e-10 4.183
DEMetro_Z 8 3.971 0.000394 3.835
DEMetro_Z 10 6.482 3e-07 6.058
DEMetro_Z 12 6.138 1.05e-06 16.587
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 -3.649 0.00103 -0.666
DEMetro_Z_vs_SMC 1 -1.452 0.157 -0.265
DEMetro_Z_vs_SMC 2 1.811 0.0804 0.331
DEMetro_Z_vs_SMC 3 0.327 0.746 0.060
DEMetro_Z_vs_SMC 4 0.553 0.584 0.101
DEMetro_Z_vs_SMC 5 1.742 0.0921 0.318
HMC_vs_Metro 0 -2.732 0.0106 -0.499
HMC_vs_Metro 1 -2.496 0.0185 -0.456
HMC_vs_Metro 2 0.512 0.613 0.093
HMC_vs_Metro 3 1.401 0.172 0.256
HMC_vs_Metro 4 1.525 0.138 0.278
HMC_vs_Metro 5 4.526 9.44e-05 0.826
Metro_vs_DEMetro_Z 0 -1.396 0.173 -0.255
Metro_vs_DEMetro_Z 1 -1.979 0.0574 -0.361
Metro_vs_DEMetro_Z 2 -3.969 0.000435 -0.725
Metro_vs_DEMetro_Z 3 -1.355 0.186 -0.247
Metro_vs_DEMetro_Z 4 -3.185 0.00345 -0.582
Metro_vs_DEMetro_Z 5 -4.086 0.000316 -0.746
HMC_vs_SMC 0 -5.424 7.81e-06 -0.990
HMC_vs_SMC 1 -4.930 3.08e-05 -0.900
HMC_vs_SMC 2 -0.644 0.525 -0.118
HMC_vs_SMC 3 0.035 0.972 0.006
HMC_vs_SMC 4 -0.429 0.671 -0.078
HMC_vs_SMC 5 1.577 0.126 0.288
Metro_vs_SMC 0 -4.112 0.000295 -0.751
Metro_vs_SMC 1 -3.704 0.000889 -0.676
Metro_vs_SMC 2 -1.388 0.176 -0.253
Metro_vs_SMC 3 -1.466 0.153 -0.268
Metro_vs_SMC 4 -2.136 0.0412 -0.390
Metro_vs_SMC 5 -4.063 0.000337 -0.742
HMC_vs_DEMetro_Z 0 -3.443 0.00177 -0.629
HMC_vs_DEMetro_Z 1 -3.654 0.00101 -0.667
HMC_vs_DEMetro_Z 2 -2.432 0.0214 -0.444
HMC_vs_DEMetro_Z 3 -0.271 0.789 -0.049
HMC_vs_DEMetro_Z 4 -1.115 0.274 -0.204
HMC_vs_DEMetro_Z 5 -0.404 0.689 -0.074
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.024 0.015 0.004 2.072
HMC 4 0.022 0.012 0.003 3.010
HMC 6 0.028 0.014 0.006 2.468
HMC 8 0.036 0.013 0.006 3.528
HMC 10 0.040 0.012 0.006 4.644
HMC 12 0.065 0.010 0.004 15.288
SMC 0 0.065 0.015 0.004 11.651
SMC 4 0.043 0.012 0.003 9.538
SMC 6 0.031 0.014 0.006 3.007
SMC 8 0.036 0.013 0.006 3.495
SMC 10 0.044 0.012 0.006 5.259
SMC 12 0.048 0.010 0.004 10.772
Metro 0 0.034 0.015 0.004 4.362
Metro 4 0.028 0.012 0.003 4.846
Metro 6 0.026 0.014 0.006 2.097
Metro 8 0.028 0.013 0.006 2.391
Metro 10 0.031 0.012 0.006 3.044
Metro 12 0.026 0.010 0.004 4.664
DEMetro_Z 0 0.038 0.015 0.004 5.438
DEMetro_Z 4 0.035 0.012 0.003 7.067
DEMetro_Z 6 0.038 0.014 0.006 4.183
DEMetro_Z 8 0.038 0.013 0.006 3.835
DEMetro_Z 10 0.049 0.012 0.006 6.058
DEMetro_Z 12 0.069 0.010 0.004 16.587
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Mode Transitions (scatter)
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Forest & Ridge Plots
Pooled
0 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
4 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
6 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
8 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
12 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
0 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
4 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
6 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
8 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
12 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
0
4
6
8
10
12
Chain
0
4
6
8
10
12

two_attr_tails

▼

Varying_Tails_with_high_Dimension (MvStudentT, nu, 30 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 2.232 0.0333 3.525
HMC 2.5 2.524 0.017 2.606
HMC 3.0 2.280 0.03 3.771
HMC 4.0 0.994 0.328 0.809
HMC 10.0 -2.533 0.0141 -0.675
HMC 50.0 -5.996 1.43e-07 -1.478
SMC 2.1 20.634 7.62e-28 5.916
SMC 2.5 28.810 7.72e-26 17.450
SMC 3.0 30.967 1.88e-25 25.278
SMC 4.0 33.603 7.19e-26 34.797
SMC 10.0 36.157 3.38e-27 32.675
SMC 50.0 15.742 3.27e-20 5.764
Metro 2.1 6.788 1.72e-07 13.232
Metro 2.5 7.176 5.74e-08 11.191
Metro 3.0 11.079 1.3e-12 8.217
Metro 4.0 4.961 2.69e-05 9.045
Metro 10.0 16.404 7.66e-18 10.199
Metro 50.0 17.607 9.3e-20 8.846
DEMetro_Z 2.1 27.477 2.55e-22 353.621
DEMetro_Z 2.5 22.298 8.42e-20 497.613
DEMetro_Z 3.0 22.965 3.73e-20 357.048
DEMetro_Z 4.0 22.081 1.09e-19 295.679
DEMetro_Z 10.0 27.094 3.78e-22 380.531
DEMetro_Z 50.0 14.460 8.6e-15 342.419
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -28.777 7.07e-23 -5.254
HMC_vs_DEMetro_Z 1 -22.249 8.97e-20 -4.062
HMC_vs_DEMetro_Z 2 -22.196 9.57e-20 -4.052
HMC_vs_DEMetro_Z 3 -22.601 5.83e-20 -4.126
HMC_vs_DEMetro_Z 4 -27.046 4.02e-22 -4.938
HMC_vs_DEMetro_Z 5 -14.506 7.94e-15 -2.648
Metro_vs_SMC 0 3.778 0.000729 0.690
Metro_vs_SMC 1 -3.612 0.00113 -0.659
Metro_vs_SMC 2 -15.562 1.3e-15 -2.841
Metro_vs_SMC 3 -10.920 8.64e-12 -1.994
Metro_vs_SMC 4 -20.660 6.8e-19 -3.772
Metro_vs_SMC 5 5.543 5.61e-06 1.012
Metro_vs_DEMetro_Z 0 -25.603 1.85e-21 -4.674
Metro_vs_DEMetro_Z 1 -21.906 1.37e-19 -3.999
Metro_vs_DEMetro_Z 2 -22.210 9.42e-20 -4.055
Metro_vs_DEMetro_Z 3 -21.643 1.91e-19 -3.951
Metro_vs_DEMetro_Z 4 -26.634 6.16e-22 -4.863
Metro_vs_DEMetro_Z 5 -14.060 1.76e-14 -2.567
HMC_vs_Metro 0 -3.536 0.00139 -0.646
HMC_vs_Metro 1 -4.558 8.64e-05 -0.832
HMC_vs_Metro 2 -2.418 0.0221 -0.441
HMC_vs_Metro 3 -4.248 0.000203 -0.776
HMC_vs_Metro 4 -16.742 1.91e-16 -3.057
HMC_vs_Metro 5 -20.245 1.18e-18 -3.696
HMC_vs_SMC 0 -1.463 0.154 -0.267
HMC_vs_SMC 1 -12.083 7.67e-13 -2.206
HMC_vs_SMC 2 -11.971 9.61e-13 -2.186
HMC_vs_SMC 3 -26.740 5.52e-22 -4.882
HMC_vs_SMC 4 -39.618 8.34e-27 -7.233
HMC_vs_SMC 5 -19.402 3.73e-18 -3.542
DEMetro_Z_vs_SMC 0 26.935 4.5e-22 4.918
DEMetro_Z_vs_SMC 1 21.826 1.52e-19 3.985
DEMetro_Z_vs_SMC 2 21.317 2.9e-19 3.892
DEMetro_Z_vs_SMC 3 19.700 2.47e-18 3.597
DEMetro_Z_vs_SMC 4 24.773 4.62e-21 4.523
DEMetro_Z_vs_SMC 5 14.150 1.5e-14 2.584
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.148 0.070 0.022 3.525
HMC 2.5 0.068 0.047 0.008 2.606
HMC 3.0 0.059 0.038 0.006 3.771
HMC 4.0 0.036 0.032 0.004 0.809
HMC 10.0 0.023 0.024 0.003 -0.675
HMC 50.0 0.019 0.022 0.002 -1.478
SMC 2.1 0.201 0.070 0.022 5.916
SMC 2.5 0.189 0.047 0.008 17.450
SMC 3.0 0.178 0.038 0.006 25.278
SMC 4.0 0.176 0.032 0.004 34.797
SMC 10.0 0.106 0.024 0.003 32.675
SMC 50.0 0.035 0.022 0.002 5.764
Metro 2.1 0.364 0.070 0.022 13.232
Metro 2.5 0.138 0.047 0.008 11.191
Metro 3.0 0.083 0.038 0.006 8.217
Metro 4.0 0.070 0.032 0.004 9.045
Metro 10.0 0.050 0.024 0.003 10.199
Metro 50.0 0.042 0.022 0.002 8.846
DEMetro_Z 2.1 7.928 0.070 0.022 353.621
DEMetro_Z 2.5 4.096 0.047 0.008 497.613
DEMetro_Z 3.0 2.018 0.038 0.006 357.048
DEMetro_Z 4.0 1.255 0.032 0.004 295.679
DEMetro_Z 10.0 0.976 0.024 0.003 380.531
DEMetro_Z 50.0 0.802 0.022 0.002 342.419
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 0.520 0.605 0.153
HMC 2.5 0.305 0.762 0.067
HMC 3.0 1.666 0.105 1.198
HMC 4.0 3.746 0.000603 1.889
HMC 10.0 5.062 1.33e-05 2.999
HMC 50.0 7.139 3.25e-09 2.318
SMC 2.1 26.482 2.44e-25 5.135
SMC 2.5 125.339 1.71e-61 44.504
SMC 3.0 103.236 5.13e-39 301.492
SMC 4.0 83.257 4.46e-36 1640.752
SMC 10.0 102.240 1.19e-38 5057.956
SMC 50.0 62.318 1.15e-32 170.777
Metro 2.1 2.683 0.0115 2.221
Metro 2.5 1.243 0.224 1.995
Metro 3.0 2.371 0.0242 2.623
Metro 4.0 1.784 0.085 12.503
Metro 10.0 11.502 6.47e-13 9.362
Metro 50.0 13.489 8.49e-16 7.132
DEMetro_Z 2.1 15.707 8.88e-16 49.350
DEMetro_Z 2.5 15.818 8.24e-16 109.657
DEMetro_Z 3.0 17.467 6.14e-17 184.667
DEMetro_Z 4.0 14.912 3.91e-15 448.141
DEMetro_Z 10.0 15.407 1.68e-15 1850.328
DEMetro_Z 50.0 7.955 8.98e-09 1556.242
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -21.286 3.01e-19 -3.886
HMC_vs_SMC 1 -126.808 2.34e-41 -23.152
HMC_vs_SMC 2 -105.321 5.05e-39 -19.229
HMC_vs_SMC 3 -83.319 4.41e-36 -15.212
HMC_vs_SMC 4 -101.940 1.3e-38 -18.612
HMC_vs_SMC 5 -61.468 2.85e-32 -11.223
Metro_vs_DEMetro_Z 0 -15.320 1.94e-15 -2.797
Metro_vs_DEMetro_Z 1 -15.059 3.03e-15 -2.749
Metro_vs_DEMetro_Z 2 -17.145 1.02e-16 -3.130
Metro_vs_DEMetro_Z 3 -14.245 1.26e-14 -2.601
Metro_vs_DEMetro_Z 4 -15.318 1.95e-15 -2.797
Metro_vs_DEMetro_Z 5 -7.923 9.73e-09 -1.447
HMC_vs_Metro 0 -2.410 0.0225 -0.440
HMC_vs_Metro 1 -1.192 0.243 -0.218
HMC_vs_Metro 2 -1.095 0.282 -0.200
HMC_vs_Metro 3 -1.493 0.146 -0.273
HMC_vs_Metro 4 -6.608 3.05e-07 -1.206
HMC_vs_Metro 5 -9.742 1.19e-10 -1.779
HMC_vs_DEMetro_Z 0 -15.669 1.08e-15 -2.861
HMC_vs_DEMetro_Z 1 -15.782 8.99e-16 -2.881
HMC_vs_DEMetro_Z 2 -17.094 1.1e-16 -3.121
HMC_vs_DEMetro_Z 3 -14.870 4.21e-15 -2.715
HMC_vs_DEMetro_Z 4 -15.388 1.74e-15 -2.809
HMC_vs_DEMetro_Z 5 -7.945 9.2e-09 -1.451
Metro_vs_SMC 0 -3.633 0.00107 -0.663
Metro_vs_SMC 1 -26.651 6.06e-22 -4.866
Metro_vs_SMC 2 -92.976 1.86e-37 -16.975
Metro_vs_SMC 3 -83.315 4.42e-36 -15.211
Metro_vs_SMC 4 -102.253 1.19e-38 -18.669
Metro_vs_SMC 5 -59.863 6.1e-32 -10.929
DEMetro_Z_vs_SMC 0 14.011 1.92e-14 2.558
DEMetro_Z_vs_SMC 1 9.426 2.48e-10 1.721
DEMetro_Z_vs_SMC 2 -9.499 2.09e-10 -1.734
DEMetro_Z_vs_SMC 3 -30.358 1.57e-23 -5.543
DEMetro_Z_vs_SMC 4 -22.977 3.7e-20 -4.195
DEMetro_Z_vs_SMC 5 7.076 8.74e-08 1.292
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 12.205 9.489 17.780 0.153
HMC 2.5 2.137 1.990 2.209 0.067
HMC 3.0 0.961 0.588 0.312 1.198
HMC 4.0 0.257 0.165 0.049 1.889
HMC 10.0 0.067 0.049 0.006 2.999
HMC 50.0 0.045 0.035 0.004 2.318
SMC 2.1 100.791 9.489 17.780 5.135
SMC 2.5 100.315 1.990 2.209 44.504
SMC 3.0 94.553 0.588 0.312 301.492
SMC 4.0 80.555 0.165 0.049 1640.752
SMC 10.0 30.888 0.049 0.006 5057.956
SMC 50.0 0.778 0.035 0.004 170.777
Metro 2.1 48.985 9.489 17.780 2.221
Metro 2.5 6.398 1.990 2.209 1.995
Metro 3.0 1.406 0.588 0.312 2.623
Metro 4.0 0.777 0.165 0.049 12.503
Metro 10.0 0.106 0.049 0.006 9.362
Metro 50.0 0.066 0.035 0.004 7.132
DEMetro_Z 2.1 886.908 9.489 17.780 49.350
DEMetro_Z 2.5 244.260 1.990 2.209 109.657
DEMetro_Z 3.0 58.143 0.588 0.312 184.667
DEMetro_Z 4.0 22.122 0.165 0.049 448.141
DEMetro_Z 10.0 11.331 0.049 0.006 1850.328
DEMetro_Z 50.0 6.806 0.035 0.004 1556.242
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 5.182 1.48e-05 11.935
HMC 2.5 6.055 1.28e-06 12.327
HMC 3.0 4.879 3.53e-05 22.893
HMC 4.0 5.556 4.98e-06 8.880
HMC 10.0 3.834 0.000451 1.820
HMC 50.0 1.435 0.157 0.382
SMC 2.1 171.936 1.31e-46 229.807
SMC 2.5 239.923 8.76e-50 630.669
SMC 3.0 167.635 6.85e-45 1746.010
SMC 4.0 139.154 1.55e-42 2045.892
SMC 10.0 159.784 2.83e-44 2423.074
SMC 50.0 66.305 2.16e-33 208.797
Metro 2.1 5.183 1.52e-05 60.680
Metro 2.5 3.598 0.00118 34.900
Metro 3.0 6.900 1.37e-07 28.945
Metro 4.0 6.716 2.23e-07 25.122
Metro 10.0 23.295 3.01e-22 15.902
Metro 50.0 20.129 3.02e-20 13.811
DEMetro_Z 2.1 32.287 2.76e-24 716.506
DEMetro_Z 2.5 30.576 1.28e-23 995.835
DEMetro_Z 3.0 32.924 1.59e-24 1272.174
DEMetro_Z 4.0 27.927 1.63e-22 897.400
DEMetro_Z 10.0 28.417 1.01e-22 1221.009
DEMetro_Z 50.0 15.232 2.26e-15 979.939
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -27.962 1.58e-22 -5.105
Metro_vs_DEMetro_Z 1 -27.453 2.64e-22 -5.012
Metro_vs_DEMetro_Z 2 -32.378 2.56e-24 -5.911
Metro_vs_DEMetro_Z 3 -27.146 3.62e-22 -4.956
Metro_vs_DEMetro_Z 4 -28.021 1.49e-22 -5.116
Metro_vs_DEMetro_Z 5 -14.992 3.4e-15 -2.737
DEMetro_Z_vs_SMC 0 21.457 2.42e-19 3.917
DEMetro_Z_vs_SMC 1 11.248 4.29e-12 2.054
DEMetro_Z_vs_SMC 2 -10.640 1.58e-11 -1.943
DEMetro_Z_vs_SMC 3 -30.339 1.6e-23 -5.539
DEMetro_Z_vs_SMC 4 -24.952 3.79e-21 -4.556
DEMetro_Z_vs_SMC 5 11.966 9.7e-13 2.185
HMC_vs_DEMetro_Z 0 -32.734 1.88e-24 -5.976
HMC_vs_DEMetro_Z 1 -30.304 1.65e-23 -5.533
HMC_vs_DEMetro_Z 2 -32.113 3.23e-24 -5.863
HMC_vs_DEMetro_Z 3 -28.013 1.5e-22 -5.115
HMC_vs_DEMetro_Z 4 -28.357 1.07e-22 -5.177
HMC_vs_DEMetro_Z 5 -15.224 2.29e-15 -2.780
HMC_vs_Metro 0 -4.075 0.000326 -0.744
HMC_vs_Metro 1 -2.310 0.0282 -0.422
HMC_vs_Metro 2 -0.914 0.368 -0.167
HMC_vs_Metro 3 -4.107 0.000299 -0.750
HMC_vs_Metro 4 -16.713 2e-16 -3.051
HMC_vs_Metro 5 -19.925 1.82e-18 -3.638
HMC_vs_SMC 0 -80.253 1.3e-35 -14.652
HMC_vs_SMC 1 -185.069 4.11e-46 -33.789
HMC_vs_SMC 2 -158.938 3.38e-44 -29.018
HMC_vs_SMC 3 -137.307 2.34e-42 -25.069
HMC_vs_SMC 4 -158.285 3.81e-44 -28.899
HMC_vs_SMC 5 -66.558 2.88e-33 -12.152
Metro_vs_SMC 0 -14.758 5.1e-15 -2.694
Metro_vs_SMC 1 -58.068 1.46e-31 -10.602
Metro_vs_SMC 2 -142.905 7.36e-43 -26.091
Metro_vs_SMC 3 -140.742 1.14e-42 -25.696
Metro_vs_SMC 4 -158.917 3.39e-44 -29.014
Metro_vs_SMC 5 -59.626 6.83e-32 -10.886
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.466 0.118 0.029 11.935
HMC 2.5 0.215 0.084 0.011 12.327
HMC 3.0 0.150 0.064 0.004 22.893
HMC 4.0 0.075 0.049 0.003 8.880
HMC 10.0 0.037 0.034 0.001 1.820
HMC 50.0 0.030 0.029 0.001 0.382
SMC 2.1 6.822 0.118 0.029 229.807
SMC 2.5 6.785 0.084 0.011 630.669
SMC 3.0 6.608 0.064 0.004 1746.010
SMC 4.0 6.095 0.049 0.003 2045.892
SMC 10.0 3.630 0.034 0.001 2423.074
SMC 50.0 0.269 0.029 0.001 208.797
Metro 2.1 1.888 0.118 0.029 60.680
Metro 2.5 0.454 0.084 0.011 34.900
Metro 3.0 0.172 0.064 0.004 28.945
Metro 4.0 0.123 0.049 0.003 25.122
Metro 10.0 0.057 0.034 0.001 15.902
Metro 50.0 0.045 0.029 0.001 13.811
DEMetro_Z 2.1 21.021 0.118 0.029 716.506
DEMetro_Z 2.5 10.665 0.084 0.011 995.835
DEMetro_Z 3.0 4.832 0.064 0.004 1272.174
DEMetro_Z 4.0 2.701 0.049 0.003 897.400
DEMetro_Z 10.0 1.846 0.034 0.001 1221.009
DEMetro_Z 50.0 1.153 0.029 0.001 979.939
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 5.821 2.59e-06 48.828
HMC 2.5 5.793 2.79e-06 29.885
HMC 3.0 4.614 7.37e-05 22.439
HMC 4.0 4.947 2.73e-05 7.293
HMC 10.0 2.795 0.00729 0.907
HMC 50.0 -0.181 0.857 -0.044
SMC 2.1 162.836 1.52e-45 251.405
SMC 2.5 183.333 6.15e-47 303.323
SMC 3.0 194.430 9.03e-48 309.901
SMC 4.0 172.441 4.77e-46 301.847
SMC 10.0 187.598 2.03e-47 284.323
SMC 50.0 64.637 6.68e-34 84.507
Metro 2.1 8.797 1.11e-09 124.659
Metro 2.5 6.895 1.41e-07 60.787
Metro 3.0 8.132 5.45e-09 25.122
Metro 4.0 14.051 1.09e-14 21.632
Metro 10.0 20.569 1.07e-21 10.962
Metro 50.0 18.762 1.17e-20 9.481
DEMetro_Z 2.1 87.765 6.99e-37 318.117
DEMetro_Z 2.5 88.113 6.72e-37 361.395
DEMetro_Z 3.0 91.626 2.02e-37 337.461
DEMetro_Z 4.0 80.861 7.74e-36 305.384
DEMetro_Z 10.0 73.338 1.38e-34 301.955
DEMetro_Z 50.0 39.670 7.63e-27 299.619
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 16.743 1.91e-16 3.057
DEMetro_Z_vs_SMC 1 11.752 1.5e-12 2.146
DEMetro_Z_vs_SMC 2 7.100 8.21e-08 1.296
DEMetro_Z_vs_SMC 3 0.857 0.398 0.156
DEMetro_Z_vs_SMC 4 3.607 0.00115 0.658
DEMetro_Z_vs_SMC 5 28.345 1.08e-22 5.175
HMC_vs_Metro 0 -4.411 0.00013 -0.805
HMC_vs_Metro 1 -3.004 0.00545 -0.548
HMC_vs_Metro 2 -0.439 0.664 -0.080
HMC_vs_Metro 3 -7.463 3.18e-08 -1.363
HMC_vs_Metro 4 -16.641 2.24e-16 -3.038
HMC_vs_Metro 5 -19.256 4.58e-18 -3.516
Metro_vs_DEMetro_Z 0 -13.544 4.53e-14 -2.473
Metro_vs_DEMetro_Z 1 -35.501 1.89e-25 -6.482
Metro_vs_DEMetro_Z 2 -63.484 1.12e-32 -11.591
Metro_vs_DEMetro_Z 3 -76.385 5.42e-35 -13.946
Metro_vs_DEMetro_Z 4 -70.594 5.27e-34 -12.889
Metro_vs_DEMetro_Z 5 -37.982 2.77e-26 -6.934
HMC_vs_SMC 0 -23.972 1.15e-20 -4.377
HMC_vs_SMC 1 -48.089 3.28e-29 -8.780
HMC_vs_SMC 2 -60.796 3.91e-32 -11.100
HMC_vs_SMC 3 -151.736 1.3e-43 -27.703
HMC_vs_SMC 4 -178.797 1.12e-45 -32.644
HMC_vs_SMC 5 -64.102 8.51e-33 -11.703
Metro_vs_SMC 0 -8.827 1.03e-09 -1.612
Metro_vs_SMC 1 -25.888 1.36e-21 -4.727
Metro_vs_SMC 2 -75.300 8.2e-35 -13.748
Metro_vs_SMC 3 -136.341 2.87e-42 -24.892
Metro_vs_SMC 4 -170.020 4.8e-45 -31.041
Metro_vs_SMC 5 -53.822 1.3e-30 -9.826
HMC_vs_DEMetro_Z 0 -26.946 4.45e-22 -4.920
HMC_vs_DEMetro_Z 1 -53.509 1.53e-30 -9.769
HMC_vs_DEMetro_Z 2 -51.620 4.31e-30 -9.424
HMC_vs_DEMetro_Z 3 -79.345 1.81e-35 -14.486
HMC_vs_DEMetro_Z 4 -73.695 1.53e-34 -13.455
HMC_vs_DEMetro_Z 5 -39.678 7.99e-27 -7.244
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.088 0.015 0.001 48.828
HMC 2.5 0.053 0.015 0.001 29.885
HMC 3.0 0.043 0.015 0.001 22.439
HMC 4.0 0.025 0.015 0.001 7.293
HMC 10.0 0.015 0.014 0.001 0.907
HMC 50.0 0.014 0.014 0.001 -0.044
SMC 2.1 0.392 0.015 0.001 251.405
SMC 2.5 0.399 0.015 0.001 303.323
SMC 3.0 0.408 0.015 0.001 309.901
SMC 4.0 0.410 0.015 0.001 301.847
SMC 10.0 0.381 0.014 0.001 284.323
SMC 50.0 0.111 0.014 0.001 84.507
Metro 2.1 0.202 0.015 0.001 124.659
Metro 2.5 0.092 0.015 0.001 60.787
Metro 3.0 0.047 0.015 0.001 25.122
Metro 4.0 0.043 0.015 0.001 21.632
Metro 10.0 0.028 0.014 0.001 10.962
Metro 50.0 0.025 0.014 0.001 9.481
DEMetro_Z 2.1 0.492 0.015 0.001 318.117
DEMetro_Z 2.5 0.473 0.015 0.001 361.395
DEMetro_Z 3.0 0.443 0.015 0.001 337.461
DEMetro_Z 4.0 0.414 0.015 0.001 305.384
DEMetro_Z 10.0 0.404 0.014 0.001 301.955
DEMetro_Z 50.0 0.357 0.014 0.001 299.619
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 1.620 0.116 7.235
HMC 2.5 1.454 0.157 5.020
HMC 3.0 1.720 0.096 4.921
HMC 4.0 -2.718 0.00878 -0.809
HMC 10.0 -1.542 0.129 -0.438
HMC 50.0 -5.897 2.03e-07 -1.476
SMC 2.1 16.497 3.63e-19 7.772
SMC 2.5 28.776 7.96e-25 21.273
SMC 3.0 24.374 1.62e-21 28.850
SMC 4.0 33.591 8.04e-26 35.498
SMC 10.0 21.312 1.34e-19 32.995
SMC 50.0 10.003 2.47e-12 4.680
Metro 2.1 5.634 3.95e-06 8.457
Metro 2.5 10.454 6.37e-12 8.021
Metro 3.0 8.894 4.5e-10 8.341
Metro 4.0 17.468 1.75e-21 6.774
Metro 10.0 18.664 6.9e-20 10.785
Metro 50.0 17.028 2.49e-19 8.463
DEMetro_Z 2.1 21.818 1.52e-19 335.434
DEMetro_Z 2.5 19.730 2.37e-18 471.028
DEMetro_Z 3.0 16.636 2.25e-16 364.157
DEMetro_Z 4.0 23.857 1.29e-20 270.061
DEMetro_Z 10.0 21.419 2.53e-19 383.275
DEMetro_Z 50.0 15.970 6.58e-16 296.183
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -20.526 8.12e-19 -3.747
HMC_vs_DEMetro_Z 1 -19.770 2.25e-18 -3.610
HMC_vs_DEMetro_Z 2 -15.968 6.62e-16 -2.915
HMC_vs_DEMetro_Z 3 -23.914 1.23e-20 -4.366
HMC_vs_DEMetro_Z 4 -21.377 2.68e-19 -3.903
HMC_vs_DEMetro_Z 5 -16.060 5.7e-16 -2.932
Metro_vs_SMC 0 0.395 0.695 0.072
Metro_vs_SMC 1 -12.404 4.03e-13 -2.265
Metro_vs_SMC 2 -13.021 1.22e-13 -2.377
Metro_vs_SMC 3 -25.349 2.44e-21 -4.628
Metro_vs_SMC 4 -13.825 2.7e-14 -2.524
Metro_vs_SMC 5 5.509 6.18e-06 1.006
Metro_vs_DEMetro_Z 0 -21.376 2.69e-19 -3.903
Metro_vs_DEMetro_Z 1 -19.118 5.55e-18 -3.490
Metro_vs_DEMetro_Z 2 -16.183 4.67e-16 -2.955
Metro_vs_DEMetro_Z 3 -23.416 2.2e-20 -4.275
Metro_vs_DEMetro_Z 4 -20.840 5.37e-19 -3.805
Metro_vs_DEMetro_Z 5 -15.473 1.5e-15 -2.825
HMC_vs_Metro 0 -0.269 0.79 -0.049
HMC_vs_Metro 1 -0.833 0.412 -0.152
HMC_vs_Metro 2 -1.208 0.237 -0.221
HMC_vs_Metro 3 -17.432 6.57e-17 -3.183
HMC_vs_Metro 4 -18.420 1.51e-17 -3.363
HMC_vs_Metro 5 -20.923 4.81e-19 -3.820
HMC_vs_SMC 0 -0.118 0.907 -0.022
HMC_vs_SMC 1 -4.648 6.75e-05 -0.849
HMC_vs_SMC 2 -9.614 1.6e-10 -1.755
HMC_vs_SMC 3 -31.990 3.6e-24 -5.841
HMC_vs_SMC 4 -22.095 1.09e-19 -4.034
HMC_vs_SMC 5 -14.873 4.18e-15 -2.715
DEMetro_Z_vs_SMC 0 21.104 3.81e-19 3.853
DEMetro_Z_vs_SMC 1 18.904 7.52e-18 3.451
DEMetro_Z_vs_SMC 2 15.314 1.97e-15 2.796
DEMetro_Z_vs_SMC 3 20.264 1.15e-18 3.700
DEMetro_Z_vs_SMC 4 19.344 4.05e-18 3.532
DEMetro_Z_vs_SMC 5 15.785 8.94e-16 2.882
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.231 0.070 0.022 7.235
HMC 2.5 0.088 0.047 0.008 5.020
HMC 3.0 0.065 0.038 0.006 4.921
HMC 4.0 0.029 0.032 0.004 -0.809
HMC 10.0 0.023 0.024 0.003 -0.438
HMC 50.0 0.019 0.022 0.002 -1.476
SMC 2.1 0.243 0.070 0.022 7.772
SMC 2.5 0.220 0.047 0.008 21.273
SMC 3.0 0.198 0.038 0.006 28.850
SMC 4.0 0.179 0.032 0.004 35.498
SMC 10.0 0.107 0.024 0.003 32.995
SMC 50.0 0.033 0.022 0.002 4.680
Metro 2.1 0.258 0.070 0.022 8.457
Metro 2.5 0.112 0.047 0.008 8.021
Metro 3.0 0.084 0.038 0.006 8.341
Metro 4.0 0.060 0.032 0.004 6.774
Metro 10.0 0.051 0.024 0.003 10.785
Metro 50.0 0.042 0.022 0.002 8.463
DEMetro_Z 2.1 7.524 0.070 0.022 335.434
DEMetro_Z 2.5 3.880 0.047 0.008 471.028
DEMetro_Z 3.0 2.057 0.038 0.006 364.157
DEMetro_Z 4.0 1.149 0.032 0.004 270.061
DEMetro_Z 10.0 0.983 0.024 0.003 383.275
DEMetro_Z 50.0 0.696 0.022 0.002 296.183
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 0.098 0.923 0.023
HMC 2.5 1.062 0.295 0.550
HMC 3.0 2.572 0.0144 1.452
HMC 4.0 3.626 0.000985 2.933
HMC 10.0 5.636 1.84e-06 2.816
HMC 50.0 8.063 7.33e-11 2.410
SMC 2.1 22.936 1.27e-29 5.277
SMC 2.5 52.280 2.27e-32 44.842
SMC 3.0 50.932 5.7e-30 291.564
SMC 4.0 48.227 3.02e-29 1544.738
SMC 10.0 30.197 1.83e-23 4121.787
SMC 50.0 25.670 1.6e-21 142.352
Metro 2.1 1.367 0.182 1.377
Metro 2.5 0.458 0.649 0.101
Metro 3.0 2.664 0.0118 1.818
Metro 4.0 5.358 7.32e-06 4.783
Metro 10.0 11.679 4.87e-13 9.917
Metro 50.0 17.436 9.94e-21 7.386
DEMetro_Z 2.1 7.256 5.28e-08 25.758
DEMetro_Z 2.5 9.786 1.05e-10 50.343
DEMetro_Z 3.0 8.549 2.03e-09 86.660
DEMetro_Z 4.0 11.929 1.04e-12 152.168
DEMetro_Z 10.0 6.776 1.94e-07 700.842
DEMetro_Z 50.0 5.613 4.62e-06 553.183
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -23.804 1.39e-20 -4.346
HMC_vs_SMC 1 -49.439 1.49e-29 -9.026
HMC_vs_SMC 2 -50.870 6.55e-30 -9.287
HMC_vs_SMC 3 -48.272 2.95e-29 -8.813
HMC_vs_SMC 4 -30.192 1.84e-23 -5.512
HMC_vs_SMC 5 -25.334 2.48e-21 -4.625
Metro_vs_DEMetro_Z 0 -7.803 1.32e-08 -1.425
Metro_vs_DEMetro_Z 1 -9.728 1.23e-10 -1.776
Metro_vs_DEMetro_Z 2 -8.513 2.22e-09 -1.554
Metro_vs_DEMetro_Z 3 -11.610 2.01e-12 -2.120
Metro_vs_DEMetro_Z 4 -6.691 2.44e-07 -1.222
Metro_vs_DEMetro_Z 5 -5.540 5.66e-06 -1.012
HMC_vs_Metro 0 -1.336 0.192 -0.244
HMC_vs_Metro 1 0.915 0.368 0.167
HMC_vs_Metro 2 -0.462 0.647 -0.084
HMC_vs_Metro 3 -1.512 0.141 -0.276
HMC_vs_Metro 4 -7.648 1.97e-08 -1.396
HMC_vs_Metro 5 -12.851 1.69e-13 -2.346
HMC_vs_DEMetro_Z 0 -7.219 6e-08 -1.318
HMC_vs_DEMetro_Z 1 -9.451 2.34e-10 -1.726
HMC_vs_DEMetro_Z 2 -8.498 2.31e-09 -1.551
HMC_vs_DEMetro_Z 3 -11.627 1.94e-12 -2.123
HMC_vs_DEMetro_Z 4 -6.754 2.06e-07 -1.233
HMC_vs_DEMetro_Z 5 -5.585 5e-06 -1.020
Metro_vs_SMC 0 -3.818 0.000654 -0.697
Metro_vs_SMC 1 -53.331 1.69e-30 -9.737
Metro_vs_SMC 2 -50.416 8.48e-30 -9.205
Metro_vs_SMC 3 -47.883 3.72e-29 -8.742
Metro_vs_SMC 4 -30.089 2.02e-23 -5.494
Metro_vs_SMC 5 -24.593 5.66e-21 -4.490
DEMetro_Z_vs_SMC 0 5.723 3.41e-06 1.045
DEMetro_Z_vs_SMC 1 1.016 0.318 0.186
DEMetro_Z_vs_SMC 2 -17.435 6.54e-17 -3.183
DEMetro_Z_vs_SMC 3 -37.446 4.15e-26 -6.837
DEMetro_Z_vs_SMC 4 -19.748 2.31e-18 -3.606
DEMetro_Z_vs_SMC 5 4.169 0.000253 0.761
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 9.904 9.489 17.780 0.023
HMC 2.5 3.204 1.990 2.209 0.550
HMC 3.0 1.040 0.588 0.312 1.452
HMC 4.0 0.309 0.165 0.049 2.933
HMC 10.0 0.066 0.049 0.006 2.816
HMC 50.0 0.045 0.035 0.004 2.410
SMC 2.1 103.311 9.489 17.780 5.277
SMC 2.5 101.062 1.990 2.209 44.842
SMC 3.0 91.459 0.588 0.312 291.564
SMC 4.0 75.851 0.165 0.049 1544.738
SMC 10.0 25.180 0.049 0.006 4121.787
SMC 50.0 0.654 0.035 0.004 142.352
Metro 2.1 33.967 9.489 17.780 1.377
Metro 2.5 2.212 1.990 2.209 0.101
Metro 3.0 1.155 0.588 0.312 1.818
Metro 4.0 0.399 0.165 0.049 4.783
Metro 10.0 0.109 0.049 0.006 9.917
Metro 50.0 0.067 0.035 0.004 7.386
DEMetro_Z 2.1 467.455 9.489 17.780 25.758
DEMetro_Z 2.5 113.215 1.990 2.209 50.343
DEMetro_Z 3.0 27.597 0.588 0.312 86.660
DEMetro_Z 4.0 7.620 0.165 0.049 152.168
DEMetro_Z 10.0 4.322 0.049 0.006 700.842
DEMetro_Z 50.0 2.441 0.035 0.004 553.183
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 3.567 0.00127 12.679
HMC 2.5 3.439 0.00178 15.519
HMC 3.0 3.877 0.000557 28.514
HMC 4.0 2.721 0.0108 5.916
HMC 10.0 3.897 0.000347 1.647
HMC 50.0 0.609 0.545 0.158
SMC 2.1 72.996 1.32e-34 229.327
SMC 2.5 89.213 5.59e-37 622.993
SMC 3.0 87.797 9.61e-37 1686.790
SMC 4.0 81.869 7.27e-36 1954.750
SMC 10.0 46.649 7.83e-29 2132.137
SMC 50.0 26.264 8.67e-22 176.587
Metro 2.1 3.083 0.00446 31.239
Metro 2.5 7.898 9.67e-09 20.521
Metro 3.0 5.620 4.51e-06 32.578
Metro 4.0 8.820 9.11e-10 17.843
Metro 10.0 19.224 4.74e-19 16.490
Metro 50.0 22.227 3.26e-22 13.222
DEMetro_Z 2.1 19.059 6.02e-18 520.306
DEMetro_Z 2.5 18.069 2.52e-17 663.069
DEMetro_Z 3.0 15.364 1.8e-15 831.852
DEMetro_Z 4.0 24.947 3.79e-21 517.075
DEMetro_Z 10.0 18.815 8.53e-18 749.813
DEMetro_Z 50.0 15.207 2.35e-15 581.079
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -20.868 5.17e-19 -3.810
Metro_vs_DEMetro_Z 1 -17.080 1.13e-16 -3.118
Metro_vs_DEMetro_Z 2 -15.187 2.44e-15 -2.773
Metro_vs_DEMetro_Z 3 -24.374 7.25e-21 -4.450
Metro_vs_DEMetro_Z 4 -18.469 1.4e-17 -3.372
Metro_vs_DEMetro_Z 5 -14.853 4.33e-15 -2.712
DEMetro_Z_vs_SMC 0 10.321 3.21e-11 1.884
DEMetro_Z_vs_SMC 1 1.038 0.308 0.189
DEMetro_Z_vs_SMC 2 -14.392 9.72e-15 -2.628
DEMetro_Z_vs_SMC 3 -41.750 1.87e-27 -7.623
DEMetro_Z_vs_SMC 4 -22.555 6.16e-20 -4.118
DEMetro_Z_vs_SMC 5 10.556 1.91e-11 1.927
HMC_vs_DEMetro_Z 0 -18.708 9.95e-18 -3.416
HMC_vs_DEMetro_Z 1 -18.046 2.61e-17 -3.295
HMC_vs_DEMetro_Z 2 -14.642 6.26e-15 -2.673
HMC_vs_DEMetro_Z 3 -24.128 9.61e-21 -4.405
HMC_vs_DEMetro_Z 4 -18.785 8.91e-18 -3.430
HMC_vs_DEMetro_Z 5 -15.206 2.36e-15 -2.776
HMC_vs_Metro 0 -1.682 0.103 -0.307
HMC_vs_Metro 1 -0.882 0.385 -0.161
HMC_vs_Metro 2 -0.561 0.579 -0.102
HMC_vs_Metro 3 -3.706 0.000883 -0.677
HMC_vs_Metro 4 -15.313 1.97e-15 -2.796
HMC_vs_Metro 5 -22.418 7.28e-20 -4.093
HMC_vs_SMC 0 -40.692 3.89e-27 -7.429
HMC_vs_SMC 1 -74.288 1.21e-34 -13.563
HMC_vs_SMC 2 -87.115 1.22e-36 -15.905
HMC_vs_SMC 3 -81.327 8.88e-36 -14.848
HMC_vs_SMC 4 -46.680 7.7e-29 -8.523
HMC_vs_SMC 5 -26.404 7.85e-22 -4.821
Metro_vs_SMC 0 -17.483 6.07e-17 -3.192
Metro_vs_SMC 1 -82.049 6.88e-36 -14.980
Metro_vs_SMC 2 -83.561 4.06e-36 -15.256
Metro_vs_SMC 3 -79.624 1.64e-35 -14.537
Metro_vs_SMC 4 -46.083 1.11e-28 -8.414
Metro_vs_SMC 5 -24.076 1.02e-20 -4.396
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.488 0.118 0.029 12.679
HMC 2.5 0.249 0.084 0.011 15.519
HMC 3.0 0.171 0.064 0.004 28.514
HMC 4.0 0.067 0.049 0.003 5.916
HMC 10.0 0.036 0.034 0.001 1.647
HMC 50.0 0.030 0.029 0.001 0.158
SMC 2.1 6.808 0.118 0.029 229.327
SMC 2.5 6.703 0.084 0.011 622.993
SMC 3.0 6.386 0.064 0.004 1686.790
SMC 4.0 5.825 0.049 0.003 1954.750
SMC 10.0 3.199 0.034 0.001 2132.137
SMC 50.0 0.232 0.029 0.001 176.587
Metro 2.1 1.029 0.118 0.029 31.239
Metro 2.5 0.302 0.084 0.011 20.521
Metro 3.0 0.186 0.064 0.004 32.578
Metro 4.0 0.102 0.049 0.003 17.843
Metro 10.0 0.058 0.034 0.001 16.490
Metro 50.0 0.044 0.029 0.001 13.222
DEMetro_Z 2.1 15.297 0.118 0.029 520.306
DEMetro_Z 2.5 7.129 0.084 0.011 663.069
DEMetro_Z 3.0 3.182 0.064 0.004 831.852
DEMetro_Z 4.0 1.577 0.049 0.003 517.075
DEMetro_Z 10.0 1.147 0.034 0.001 749.813
DEMetro_Z 50.0 0.696 0.029 0.001 581.079
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 2.752 0.0101 65.153
HMC 2.5 2.640 0.0132 34.880
HMC 3.0 3.323 0.00242 28.382
HMC 4.0 2.629 0.0134 4.505
HMC 10.0 2.982 0.00439 0.975
HMC 50.0 -1.232 0.223 -0.296
SMC 2.1 136.359 6.54e-43 259.847
SMC 2.5 152.519 2.98e-44 313.107
SMC 3.0 155.527 1.67e-44 318.585
SMC 4.0 166.160 1.69e-45 304.653
SMC 10.0 168.770 7.33e-46 280.634
SMC 50.0 29.071 3.63e-23 72.818
Metro 2.1 7.794 1.35e-08 87.212
Metro 2.5 9.658 1.41e-10 52.644
Metro 3.0 7.178 6.55e-08 31.868
Metro 4.0 10.562 1.41e-11 17.313
Metro 10.0 20.031 8.26e-21 11.751
Metro 50.0 18.503 1.7e-20 9.281
DEMetro_Z 2.1 43.625 5.09e-28 352.755
DEMetro_Z 2.5 68.589 1.07e-33 392.751
DEMetro_Z 3.0 44.935 2.18e-28 352.584
DEMetro_Z 4.0 38.533 1.75e-26 294.440
DEMetro_Z 10.0 41.523 2.06e-27 294.646
DEMetro_Z 50.0 27.438 2.62e-22 250.495
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 10.748 1.25e-11 1.962
DEMetro_Z_vs_SMC 1 13.799 2.83e-14 2.519
DEMetro_Z_vs_SMC 2 4.227 0.000215 0.772
DEMetro_Z_vs_SMC 3 -1.313 0.199 -0.240
DEMetro_Z_vs_SMC 4 1.892 0.0685 0.345
DEMetro_Z_vs_SMC 5 18.842 8.21e-18 3.440
HMC_vs_Metro 0 -0.832 0.412 -0.152
HMC_vs_Metro 1 -1.147 0.261 -0.209
HMC_vs_Metro 2 -0.437 0.666 -0.080
HMC_vs_Metro 3 -4.943 2.97e-05 -0.903
HMC_vs_Metro 4 -17.683 4.49e-17 -3.228
HMC_vs_Metro 5 -18.572 1.21e-17 -3.391
Metro_vs_DEMetro_Z 0 -18.290 1.82e-17 -3.339
Metro_vs_DEMetro_Z 1 -43.809 4.73e-28 -7.998
Metro_vs_DEMetro_Z 2 -41.345 2.47e-27 -7.549
Metro_vs_DEMetro_Z 3 -36.411 9.21e-26 -6.648
Metro_vs_DEMetro_Z 4 -40.509 4.43e-27 -7.396
Metro_vs_DEMetro_Z 5 -26.438 7.57e-22 -4.827
HMC_vs_SMC 0 -8.389 3.03e-09 -1.532
HMC_vs_SMC 1 -21.538 2.18e-19 -3.932
HMC_vs_SMC 2 -33.231 1.23e-24 -6.067
HMC_vs_SMC 3 -118.631 1.61e-40 -21.659
HMC_vs_SMC 4 -166.927 8.17e-45 -30.477
HMC_vs_SMC 5 -29.480 3.59e-23 -5.382
Metro_vs_SMC 0 -15.109 2.79e-15 -2.759
Metro_vs_SMC 1 -48.578 2.46e-29 -8.869
Metro_vs_SMC 2 -57.028 2.46e-31 -10.412
Metro_vs_SMC 3 -108.530 2.12e-39 -19.815
Metro_vs_SMC 4 -152.847 1.05e-43 -27.906
Metro_vs_SMC 5 -24.665 5.22e-21 -4.503
HMC_vs_DEMetro_Z 0 -10.673 1.48e-11 -1.949
HMC_vs_DEMetro_Z 1 -23.709 1.56e-20 -4.329
HMC_vs_DEMetro_Z 2 -25.517 2.03e-21 -4.659
HMC_vs_DEMetro_Z 3 -36.324 9.85e-26 -6.632
HMC_vs_DEMetro_Z 4 -41.672 1.97e-27 -7.608
HMC_vs_DEMetro_Z 5 -27.505 2.51e-22 -5.022
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.113 0.015 0.001 65.153
HMC 2.5 0.059 0.015 0.001 34.880
HMC 3.0 0.051 0.015 0.001 28.382
HMC 4.0 0.021 0.015 0.001 4.505
HMC 10.0 0.015 0.014 0.001 0.975
HMC 50.0 0.013 0.014 0.001 -0.296
SMC 2.1 0.405 0.015 0.001 259.847
SMC 2.5 0.412 0.015 0.001 313.107
SMC 3.0 0.419 0.015 0.001 318.585
SMC 4.0 0.413 0.015 0.001 304.653
SMC 10.0 0.377 0.014 0.001 280.634
SMC 50.0 0.097 0.014 0.001 72.818
Metro 2.1 0.146 0.015 0.001 87.212
Metro 2.5 0.082 0.015 0.001 52.644
Metro 3.0 0.055 0.015 0.001 31.868
Metro 4.0 0.038 0.015 0.001 17.313
Metro 10.0 0.029 0.014 0.001 11.751
Metro 50.0 0.024 0.014 0.001 9.281
DEMetro_Z 2.1 0.544 0.015 0.001 352.755
DEMetro_Z 2.5 0.513 0.015 0.001 392.751
DEMetro_Z 3.0 0.462 0.015 0.001 352.584
DEMetro_Z 4.0 0.400 0.015 0.001 294.440
DEMetro_Z 10.0 0.395 0.014 0.001 294.646
DEMetro_Z 50.0 0.301 0.014 0.001 250.495
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Forest & Ridge Plots
Pooled
2.1 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
2.5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
4 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
50 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2.1 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
2.5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
4 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
50 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2.1
2.5
3
4
10
50
Chain
2.1
2.5
3
4
10
50

Varying_Tails_with_high_Correlation (MvStudentT, nu, 30 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 1.705 0.0944 0.569
HMC 2.5 3.108 0.00341 1.332
HMC 3.0 2.990 0.00488 1.480
HMC 4.0 1.707 0.0933 0.487
HMC 10.0 4.318 8.55e-05 1.639
HMC 50.0 2.442 0.0184 0.876
SMC 2.1 -0.386 0.701 -0.094
SMC 2.5 1.340 0.186 0.442
SMC 3.0 -0.450 0.655 -0.119
SMC 4.0 0.281 0.779 0.067
SMC 10.0 0.386 0.701 0.112
SMC 50.0 -1.288 0.204 -0.284
Metro 2.1 4.731 4.78e-05 5.360
Metro 2.5 5.105 1.8e-05 9.271
Metro 3.0 6.703 2.08e-07 10.865
Metro 4.0 5.566 4.56e-06 6.822
Metro 10.0 6.376 5.25e-07 12.145
Metro 50.0 6.312 5.04e-07 6.246
DEMetro_Z 2.1 3.904 0.00045 3.004
DEMetro_Z 2.5 2.559 0.0159 5.054
DEMetro_Z 3.0 3.568 0.00106 2.095
DEMetro_Z 4.0 3.750 0.000532 1.552
DEMetro_Z 10.0 4.341 0.000108 2.330
DEMetro_Z 50.0 3.498 0.00102 1.227
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -3.110 0.00417 -0.568
HMC_vs_DEMetro_Z 1 -1.804 0.0816 -0.329
HMC_vs_DEMetro_Z 2 -0.945 0.352 -0.173
HMC_vs_DEMetro_Z 3 -2.287 0.0297 -0.418
HMC_vs_DEMetro_Z 4 -1.480 0.15 -0.270
HMC_vs_DEMetro_Z 5 -0.749 0.46 -0.137
Metro_vs_SMC 0 4.826 4.11e-05 0.881
Metro_vs_SMC 1 4.927 3.11e-05 0.900
Metro_vs_SMC 2 6.525 3.81e-07 1.191
Metro_vs_SMC 3 5.406 8.2e-06 0.987
Metro_vs_SMC 4 6.318 6.69e-07 1.153
Metro_vs_SMC 5 6.409 5.23e-07 1.170
Metro_vs_DEMetro_Z 0 1.669 0.106 0.305
Metro_vs_DEMetro_Z 1 1.526 0.138 0.279
Metro_vs_DEMetro_Z 2 5.064 2.13e-05 0.924
Metro_vs_DEMetro_Z 3 4.214 0.000223 0.769
Metro_vs_DEMetro_Z 4 4.806 4.35e-05 0.877
Metro_vs_DEMetro_Z 5 5.408 8.17e-06 0.987
HMC_vs_Metro 0 -4.325 0.000164 -0.790
HMC_vs_Metro 1 -4.273 0.00019 -0.780
HMC_vs_Metro 2 -5.265 1.22e-05 -0.961
HMC_vs_Metro 3 -5.292 1.13e-05 -0.966
HMC_vs_Metro 4 -5.327 1.02e-05 -0.973
HMC_vs_Metro 5 -5.048 2.22e-05 -0.922
HMC_vs_SMC 0 2.255 0.0318 0.412
HMC_vs_SMC 1 2.019 0.0528 0.369
HMC_vs_SMC 2 3.235 0.00303 0.591
HMC_vs_SMC 3 1.563 0.129 0.285
HMC_vs_SMC 4 3.674 0.000961 0.671
HMC_vs_SMC 5 3.762 0.00076 0.687
DEMetro_Z_vs_SMC 0 4.188 0.00024 0.765
DEMetro_Z_vs_SMC 1 2.273 0.0306 0.415
DEMetro_Z_vs_SMC 2 3.737 0.000813 0.682
DEMetro_Z_vs_SMC 3 3.599 0.00118 0.657
DEMetro_Z_vs_SMC 4 3.752 0.000782 0.685
DEMetro_Z_vs_SMC 5 4.863 3.71e-05 0.888
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.087 0.062 0.045 0.569
HMC 2.5 0.066 0.035 0.023 1.332
HMC 3.0 0.066 0.034 0.022 1.480
HMC 4.0 0.039 0.027 0.024 0.487
HMC 10.0 0.033 0.016 0.010 1.639
HMC 50.0 0.036 0.021 0.017 0.876
SMC 2.1 0.058 0.062 0.045 -0.094
SMC 2.5 0.045 0.035 0.023 0.442
SMC 3.0 0.031 0.034 0.022 -0.119
SMC 4.0 0.029 0.027 0.024 0.067
SMC 10.0 0.017 0.016 0.010 0.112
SMC 50.0 0.016 0.021 0.017 -0.284
Metro 2.1 0.301 0.062 0.045 5.360
Metro 2.5 0.249 0.035 0.023 9.271
Metro 3.0 0.272 0.034 0.022 10.865
Metro 4.0 0.188 0.027 0.024 6.822
Metro 10.0 0.142 0.016 0.010 12.145
Metro 50.0 0.124 0.021 0.017 6.246
DEMetro_Z 2.1 0.196 0.062 0.045 3.004
DEMetro_Z 2.5 0.152 0.035 0.023 5.054
DEMetro_Z 3.0 0.079 0.034 0.022 2.095
DEMetro_Z 4.0 0.064 0.027 0.024 1.552
DEMetro_Z 10.0 0.040 0.016 0.010 2.330
DEMetro_Z 50.0 0.041 0.021 0.017 1.227
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 -1.132 0.265 -0.223
HMC 2.5 1.499 0.142 0.656
HMC 3.0 1.949 0.0595 1.190
HMC 4.0 3.060 0.00413 1.625
HMC 10.0 2.047 0.0471 0.884
HMC 50.0 2.193 0.0333 0.787
SMC 2.1 -1.900 0.0662 -0.358
SMC 2.5 -0.369 0.714 -0.142
SMC 3.0 -0.026 0.979 -0.006
SMC 4.0 -0.969 0.336 -0.252
SMC 10.0 0.302 0.763 0.081
SMC 50.0 0.027 0.979 0.007
Metro 2.1 -0.494 0.624 -0.104
Metro 2.5 1.306 0.197 0.379
Metro 3.0 2.531 0.0141 0.620
Metro 4.0 4.411 0.00012 5.379
Metro 10.0 6.177 7.88e-07 6.961
Metro 50.0 5.952 1e-06 3.877
DEMetro_Z 2.1 -0.950 0.349 -0.183
DEMetro_Z 2.5 0.831 0.412 0.507
DEMetro_Z 3.0 1.570 0.122 0.351
DEMetro_Z 4.0 4.755 2.49e-05 2.079
DEMetro_Z 10.0 4.077 0.000222 1.977
DEMetro_Z 50.0 3.060 0.0034 0.874
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 2.573 0.0155 0.470
HMC_vs_SMC 1 1.475 0.151 0.269
HMC_vs_SMC 2 2.064 0.0481 0.377
HMC_vs_SMC 3 4.358 0.00015 0.796
HMC_vs_SMC 4 1.920 0.0648 0.350
HMC_vs_SMC 5 2.047 0.0498 0.374
Metro_vs_DEMetro_Z 0 0.700 0.49 0.128
Metro_vs_DEMetro_Z 1 -0.199 0.843 -0.036
Metro_vs_DEMetro_Z 2 1.295 0.206 0.236
Metro_vs_DEMetro_Z 3 2.537 0.0168 0.463
Metro_vs_DEMetro_Z 4 4.521 9.59e-05 0.825
Metro_vs_DEMetro_Z 5 4.390 0.000138 0.801
HMC_vs_Metro 0 -1.053 0.301 -0.192
HMC_vs_Metro 1 0.758 0.455 0.138
HMC_vs_Metro 2 1.095 0.283 0.200
HMC_vs_Metro 3 -2.824 0.00849 -0.516
HMC_vs_Metro 4 -4.939 3.01e-05 -0.902
HMC_vs_Metro 5 -4.090 0.000313 -0.747
HMC_vs_DEMetro_Z 0 -0.867 0.393 -0.158
HMC_vs_DEMetro_Z 1 0.205 0.839 0.037
HMC_vs_DEMetro_Z 2 1.431 0.163 0.261
HMC_vs_DEMetro_Z 3 -0.695 0.492 -0.127
HMC_vs_DEMetro_Z 4 -2.114 0.0433 -0.386
HMC_vs_DEMetro_Z 5 -0.223 0.825 -0.041
Metro_vs_SMC 0 2.489 0.0188 0.454
Metro_vs_SMC 1 1.256 0.219 0.229
Metro_vs_SMC 2 3.317 0.00246 0.606
Metro_vs_SMC 3 4.674 6.28e-05 0.853
Metro_vs_SMC 4 6.200 9.21e-07 1.132
Metro_vs_SMC 5 5.491 6.49e-06 1.002
DEMetro_Z_vs_SMC 0 3.865 0.000576 0.706
DEMetro_Z_vs_SMC 1 0.924 0.363 0.169
DEMetro_Z_vs_SMC 2 4.553 8.78e-05 0.831
DEMetro_Z_vs_SMC 3 5.674 3.91e-06 1.036
DEMetro_Z_vs_SMC 4 3.516 0.00146 0.642
DEMetro_Z_vs_SMC 5 3.082 0.00447 0.563
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 4.442 7.653 14.425 -0.223
HMC 2.5 2.313 1.426 1.353 0.656
HMC 3.0 1.527 0.472 0.886 1.190
HMC 4.0 0.290 0.142 0.091 1.625
HMC 10.0 0.058 0.037 0.023 0.884
HMC 50.0 0.047 0.030 0.022 0.787
SMC 2.1 2.484 7.653 14.425 -0.358
SMC 2.5 1.234 1.426 1.353 -0.142
SMC 3.0 0.467 0.472 0.886 -0.006
SMC 4.0 0.119 0.142 0.091 -0.252
SMC 10.0 0.039 0.037 0.023 0.081
SMC 50.0 0.030 0.030 0.022 0.007
Metro 2.1 6.150 7.653 14.425 -0.104
Metro 2.5 1.938 1.426 1.353 0.379
Metro 3.0 1.022 0.472 0.886 0.620
Metro 4.0 0.634 0.142 0.091 5.379
Metro 10.0 0.199 0.037 0.023 6.961
Metro 50.0 0.115 0.030 0.022 3.877
DEMetro_Z 2.1 5.008 7.653 14.425 -0.183
DEMetro_Z 2.5 2.111 1.426 1.353 0.507
DEMetro_Z 3.0 0.783 0.472 0.886 0.351
DEMetro_Z 4.0 0.332 0.142 0.091 2.079
DEMetro_Z 10.0 0.083 0.037 0.023 1.977
DEMetro_Z 50.0 0.049 0.030 0.022 0.874
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 4.030 0.000185 1.306
HMC 2.5 4.366 0.000123 3.544
HMC 3.0 3.519 0.00133 3.019
HMC 4.0 5.533 1.13e-06 1.827
HMC 10.0 6.199 2.37e-07 2.736
HMC 50.0 3.327 0.00185 1.409
SMC 2.1 -1.413 0.164 -0.311
SMC 2.5 -1.248 0.218 -0.404
SMC 3.0 -0.514 0.609 -0.126
SMC 4.0 0.396 0.693 0.104
SMC 10.0 0.705 0.484 0.225
SMC 50.0 -1.671 0.101 -0.378
Metro 2.1 7.302 3.76e-08 9.263
Metro 2.5 8.564 1.66e-09 15.485
Metro 3.0 10.767 8.53e-12 16.568
Metro 4.0 9.629 1.06e-10 12.970
Metro 10.0 9.366 2.52e-10 21.200
Metro 50.0 7.931 6.62e-09 9.048
DEMetro_Z 2.1 6.740 1.34e-07 5.738
DEMetro_Z 2.5 3.398 0.00196 7.135
DEMetro_Z 3.0 7.011 3.76e-08 4.197
DEMetro_Z 4.0 8.301 2.59e-10 3.600
DEMetro_Z 10.0 7.336 1.74e-08 4.830
DEMetro_Z 50.0 5.899 3.67e-07 2.087
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 2.253 0.032 0.411
Metro_vs_DEMetro_Z 1 3.012 0.00534 0.550
Metro_vs_DEMetro_Z 2 7.113 7.93e-08 1.299
Metro_vs_DEMetro_Z 3 6.565 3.42e-07 1.199
Metro_vs_DEMetro_Z 4 6.473 4.39e-07 1.182
Metro_vs_DEMetro_Z 5 6.666 2.61e-07 1.217
DEMetro_Z_vs_SMC 0 7.246 5.59e-08 1.323
DEMetro_Z_vs_SMC 1 3.529 0.00141 0.644
DEMetro_Z_vs_SMC 2 7.354 4.22e-08 1.343
DEMetro_Z_vs_SMC 3 7.713 1.66e-08 1.408
DEMetro_Z_vs_SMC 4 6.685 2.48e-07 1.220
DEMetro_Z_vs_SMC 5 7.504 2.85e-08 1.370
HMC_vs_DEMetro_Z 0 -5.611 4.65e-06 -1.025
HMC_vs_DEMetro_Z 1 -1.625 0.115 -0.297
HMC_vs_DEMetro_Z 2 -1.302 0.203 -0.238
HMC_vs_DEMetro_Z 3 -3.286 0.00266 -0.600
HMC_vs_DEMetro_Z 4 -3.265 0.00281 -0.596
HMC_vs_DEMetro_Z 5 -1.343 0.19 -0.245
HMC_vs_Metro 0 -6.582 3.27e-07 -1.202
HMC_vs_Metro 1 -7.087 8.5e-08 -1.294
HMC_vs_Metro 2 -7.292 4.96e-08 -1.331
HMC_vs_Metro 3 -8.110 6.07e-09 -1.481
HMC_vs_Metro 4 -7.900 1.03e-08 -1.442
HMC_vs_Metro 5 -6.215 8.85e-07 -1.135
HMC_vs_SMC 0 5.706 3.58e-06 1.042
HMC_vs_SMC 1 4.737 5.26e-05 0.865
HMC_vs_SMC 2 3.650 0.00102 0.666
HMC_vs_SMC 3 6.056 1.37e-06 1.106
HMC_vs_SMC 4 4.808 4.33e-05 0.878
HMC_vs_SMC 5 5.046 2.23e-05 0.921
Metro_vs_SMC 0 7.479 3.04e-08 1.366
Metro_vs_SMC 1 8.833 1.02e-09 1.613
Metro_vs_SMC 2 11.026 6.88e-12 2.013
Metro_vs_SMC 3 9.375 2.79e-10 1.712
Metro_vs_SMC 4 9.018 6.53e-10 1.646
Metro_vs_SMC 5 8.125 5.84e-09 1.483
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.169 0.117 0.040 1.306
HMC 2.5 0.143 0.083 0.017 3.544
HMC 3.0 0.109 0.063 0.015 3.019
HMC 4.0 0.073 0.045 0.015 1.827
HMC 10.0 0.046 0.029 0.006 2.736
HMC 50.0 0.045 0.030 0.011 1.409
SMC 2.1 0.104 0.117 0.040 -0.311
SMC 2.5 0.076 0.083 0.017 -0.404
SMC 3.0 0.061 0.063 0.015 -0.126
SMC 4.0 0.047 0.045 0.015 0.104
SMC 10.0 0.030 0.029 0.006 0.225
SMC 50.0 0.026 0.030 0.011 -0.378
Metro 2.1 0.487 0.117 0.040 9.263
Metro 2.5 0.346 0.083 0.017 15.485
Metro 3.0 0.319 0.063 0.015 16.568
Metro 4.0 0.242 0.045 0.015 12.970
Metro 10.0 0.161 0.029 0.006 21.200
Metro 50.0 0.127 0.030 0.011 9.048
DEMetro_Z 2.1 0.346 0.117 0.040 5.738
DEMetro_Z 2.5 0.204 0.083 0.017 7.135
DEMetro_Z 3.0 0.127 0.063 0.015 4.197
DEMetro_Z 4.0 0.100 0.045 0.015 3.600
DEMetro_Z 10.0 0.059 0.029 0.006 4.830
DEMetro_Z 50.0 0.053 0.030 0.011 2.087
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 4.990 1.04e-05 2.007
HMC 2.5 3.964 0.000308 1.894
HMC 3.0 3.146 0.00296 1.219
HMC 4.0 4.830 1.45e-05 1.709
HMC 10.0 5.183 4.32e-06 1.819
HMC 50.0 3.426 0.00132 1.311
SMC 2.1 0.798 0.428 0.213
SMC 2.5 -0.393 0.696 -0.103
SMC 3.0 -0.392 0.697 -0.094
SMC 4.0 0.939 0.352 0.271
SMC 10.0 -0.146 0.885 -0.041
SMC 50.0 -1.603 0.114 -0.388
Metro 2.1 11.199 2.99e-12 15.272
Metro 2.5 9.959 5.63e-11 16.822
Metro 3.0 9.510 1.41e-10 12.810
Metro 4.0 10.118 2.57e-11 10.552
Metro 10.0 10.118 3.38e-11 13.679
Metro 50.0 8.933 4.31e-10 8.758
DEMetro_Z 2.1 7.548 1.85e-08 8.752
DEMetro_Z 2.5 6.625 1.96e-07 6.024
DEMetro_Z 3.0 7.201 1.09e-08 3.340
DEMetro_Z 4.0 8.670 4.75e-11 3.421
DEMetro_Z 10.0 5.778 1.22e-06 2.957
DEMetro_Z 50.0 5.468 1.72e-06 1.977
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 7.454 3.25e-08 1.361
DEMetro_Z_vs_SMC 1 6.897 1.41e-07 1.259
DEMetro_Z_vs_SMC 2 7.838 1.21e-08 1.431
DEMetro_Z_vs_SMC 3 7.458 3.22e-08 1.362
DEMetro_Z_vs_SMC 4 5.864 2.31e-06 1.071
DEMetro_Z_vs_SMC 5 7.113 7.93e-08 1.299
HMC_vs_Metro 0 -10.361 2.93e-11 -1.892
HMC_vs_Metro 1 -8.602 1.79e-09 -1.570
HMC_vs_Metro 2 -7.948 9.14e-09 -1.451
HMC_vs_Metro 3 -8.475 2.44e-09 -1.547
HMC_vs_Metro 4 -8.315 3.64e-09 -1.518
HMC_vs_Metro 5 -7.139 7.4e-08 -1.303
Metro_vs_DEMetro_Z 0 3.552 0.00133 0.648
Metro_vs_DEMetro_Z 1 5.802 2.75e-06 1.059
Metro_vs_DEMetro_Z 2 7.165 6.91e-08 1.308
Metro_vs_DEMetro_Z 3 6.240 8.27e-07 1.139
Metro_vs_DEMetro_Z 4 7.236 5.74e-08 1.321
Metro_vs_DEMetro_Z 5 7.100 8.22e-08 1.296
HMC_vs_SMC 0 4.061 0.000339 0.741
HMC_vs_SMC 1 4.212 0.000224 0.769
HMC_vs_SMC 2 3.456 0.00171 0.631
HMC_vs_SMC 3 4.930 3.09e-05 0.900
HMC_vs_SMC 4 4.713 5.64e-05 0.860
HMC_vs_SMC 5 4.988 2.62e-05 0.911
Metro_vs_SMC 0 10.789 1.15e-11 1.970
Metro_vs_SMC 1 9.934 7.67e-11 1.814
Metro_vs_SMC 2 9.615 1.6e-10 1.755
Metro_vs_SMC 3 9.465 2.26e-10 1.728
Metro_vs_SMC 4 9.696 1.32e-10 1.770
Metro_vs_SMC 5 9.308 3.27e-10 1.699
HMC_vs_DEMetro_Z 0 -5.546 5.58e-06 -1.012
HMC_vs_DEMetro_Z 1 -4.195 0.000235 -0.766
HMC_vs_DEMetro_Z 2 -3.730 0.000828 -0.681
HMC_vs_DEMetro_Z 3 -3.514 0.00147 -0.641
HMC_vs_DEMetro_Z 4 -2.168 0.0385 -0.396
HMC_vs_DEMetro_Z 5 -1.355 0.186 -0.247
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.026 0.015 0.006 2.007
HMC 2.5 0.024 0.016 0.005 1.894
HMC 3.0 0.022 0.015 0.006 1.219
HMC 4.0 0.024 0.014 0.006 1.709
HMC 10.0 0.022 0.013 0.005 1.819
HMC 50.0 0.023 0.015 0.006 1.311
SMC 2.1 0.016 0.015 0.006 0.213
SMC 2.5 0.015 0.016 0.005 -0.103
SMC 3.0 0.015 0.015 0.006 -0.094
SMC 4.0 0.015 0.014 0.006 0.271
SMC 10.0 0.013 0.013 0.005 -0.041
SMC 50.0 0.013 0.015 0.006 -0.388
Metro 2.1 0.103 0.015 0.006 15.272
Metro 2.5 0.091 0.016 0.005 16.822
Metro 3.0 0.086 0.015 0.006 12.810
Metro 4.0 0.077 0.014 0.006 10.552
Metro 10.0 0.080 0.013 0.005 13.679
Metro 50.0 0.066 0.015 0.006 8.758
DEMetro_Z 2.1 0.065 0.015 0.006 8.752
DEMetro_Z 2.5 0.043 0.016 0.005 6.024
DEMetro_Z 3.0 0.034 0.015 0.006 3.340
DEMetro_Z 4.0 0.034 0.014 0.006 3.421
DEMetro_Z 10.0 0.028 0.013 0.005 2.957
DEMetro_Z 50.0 0.027 0.015 0.006 1.977
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 1.717 0.0938 0.790
HMC 2.5 2.502 0.0164 1.066
HMC 3.0 2.096 0.042 0.852
HMC 4.0 2.834 0.00673 1.003
HMC 10.0 3.119 0.00334 1.375
HMC 50.0 1.844 0.0719 0.708
SMC 2.1 -0.203 0.84 -0.051
SMC 2.5 0.579 0.565 0.184
SMC 3.0 -0.766 0.447 -0.193
SMC 4.0 -0.692 0.492 -0.147
SMC 10.0 -0.756 0.453 -0.185
SMC 50.0 -1.083 0.284 -0.241
Metro 2.1 6.378 3.37e-07 4.813
Metro 2.5 6.895 1.31e-07 14.481
Metro 3.0 6.401 4.39e-07 7.934
Metro 4.0 5.494 5.32e-06 5.789
Metro 10.0 6.857 1.33e-07 10.165
Metro 50.0 5.434 6.34e-06 5.806
DEMetro_Z 2.1 2.243 0.0297 0.821
DEMetro_Z 2.5 4.461 9.77e-05 4.086
DEMetro_Z 3.0 3.438 0.00151 1.972
DEMetro_Z 4.0 4.134 0.000167 1.733
DEMetro_Z 10.0 5.307 5.12e-06 2.634
DEMetro_Z 50.0 1.645 0.106 0.447
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -0.071 0.944 -0.013
HMC_vs_DEMetro_Z 1 -3.266 0.0028 -0.596
HMC_vs_DEMetro_Z 2 -1.830 0.0775 -0.334
HMC_vs_DEMetro_Z 3 -1.519 0.14 -0.277
HMC_vs_DEMetro_Z 4 -2.801 0.00899 -0.511
HMC_vs_DEMetro_Z 5 0.750 0.459 0.137
Metro_vs_SMC 0 6.321 6.62e-07 1.154
Metro_vs_SMC 1 6.483 4.28e-07 1.184
Metro_vs_SMC 2 6.615 3e-07 1.208
Metro_vs_SMC 3 5.624 4.49e-06 1.027
Metro_vs_SMC 4 7.155 7.1e-08 1.306
Metro_vs_SMC 5 5.719 3.45e-06 1.044
Metro_vs_DEMetro_Z 0 5.348 9.64e-06 0.976
Metro_vs_DEMetro_Z 1 4.788 4.57e-05 0.874
Metro_vs_DEMetro_Z 2 4.395 0.000136 0.802
Metro_vs_DEMetro_Z 3 3.592 0.0012 0.656
Metro_vs_DEMetro_Z 4 5.201 1.45e-05 0.950
Metro_vs_DEMetro_Z 5 4.946 2.95e-05 0.903
HMC_vs_Metro 0 -4.695 5.92e-05 -0.857
HMC_vs_Metro 1 -5.842 2.46e-06 -1.067
HMC_vs_Metro 2 -5.427 7.75e-06 -0.991
HMC_vs_Metro 3 -4.367 0.000147 -0.797
HMC_vs_Metro 4 -5.821 2.6e-06 -1.063
HMC_vs_Metro 5 -4.571 8.34e-05 -0.835
HMC_vs_SMC 0 1.774 0.0866 0.324
HMC_vs_SMC 1 1.883 0.0698 0.344
HMC_vs_SMC 2 3.469 0.00165 0.633
HMC_vs_SMC 3 3.205 0.00327 0.585
HMC_vs_SMC 4 3.542 0.00136 0.647
HMC_vs_SMC 5 2.508 0.018 0.458
DEMetro_Z_vs_SMC 0 2.241 0.0329 0.409
DEMetro_Z_vs_SMC 1 4.202 0.000231 0.767
DEMetro_Z_vs_SMC 2 3.854 0.000594 0.704
DEMetro_Z_vs_SMC 3 4.542 9.05e-05 0.829
DEMetro_Z_vs_SMC 4 5.753 3.15e-06 1.050
DEMetro_Z_vs_SMC 5 2.934 0.00648 0.536
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.097 0.062 0.045 0.790
HMC 2.5 0.060 0.035 0.023 1.066
HMC 3.0 0.052 0.034 0.022 0.852
HMC 4.0 0.051 0.027 0.024 1.003
HMC 10.0 0.030 0.016 0.010 1.375
HMC 50.0 0.033 0.021 0.017 0.708
SMC 2.1 0.060 0.062 0.045 -0.051
SMC 2.5 0.039 0.035 0.023 0.184
SMC 3.0 0.029 0.034 0.022 -0.193
SMC 4.0 0.024 0.027 0.024 -0.147
SMC 10.0 0.014 0.016 0.010 -0.185
SMC 50.0 0.017 0.021 0.017 -0.241
Metro 2.1 0.276 0.062 0.045 4.813
Metro 2.5 0.370 0.035 0.023 14.481
Metro 3.0 0.207 0.034 0.022 7.934
Metro 4.0 0.164 0.027 0.024 5.789
Metro 10.0 0.122 0.016 0.010 10.165
Metro 50.0 0.117 0.021 0.017 5.806
DEMetro_Z 2.1 0.099 0.062 0.045 0.821
DEMetro_Z 2.5 0.130 0.035 0.023 4.086
DEMetro_Z 3.0 0.077 0.034 0.022 1.972
DEMetro_Z 4.0 0.068 0.027 0.024 1.733
DEMetro_Z 10.0 0.043 0.016 0.010 2.634
DEMetro_Z 50.0 0.029 0.021 0.017 0.447
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 -1.576 0.125 -0.293
HMC 2.5 1.021 0.314 0.453
HMC 3.0 1.108 0.273 0.251
HMC 4.0 2.009 0.051 0.832
HMC 10.0 3.350 0.00179 1.541
HMC 50.0 3.259 0.00219 1.312
SMC 2.1 -1.493 0.144 -0.288
SMC 2.5 -0.928 0.357 -0.244
SMC 3.0 0.134 0.894 0.028
SMC 4.0 0.664 0.509 0.173
SMC 10.0 0.012 0.99 0.003
SMC 50.0 -0.177 0.86 -0.046
Metro 2.1 -1.067 0.294 -0.202
Metro 2.5 1.473 0.146 0.394
Metro 3.0 3.223 0.00218 0.723
Metro 4.0 4.269 0.000171 4.127
Metro 10.0 6.007 1.26e-06 6.704
Metro 50.0 5.811 2.17e-06 6.259
DEMetro_Z 2.1 -1.220 0.231 -0.233
DEMetro_Z 2.5 1.119 0.268 0.310
DEMetro_Z 3.0 1.704 0.0941 0.396
DEMetro_Z 4.0 3.463 0.00127 1.522
DEMetro_Z 10.0 3.461 0.00152 2.591
DEMetro_Z 50.0 3.037 0.00389 1.091
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -0.075 0.941 -0.014
HMC_vs_SMC 1 1.526 0.138 0.279
HMC_vs_SMC 2 1.603 0.12 0.293
HMC_vs_SMC 3 1.550 0.132 0.283
HMC_vs_SMC 4 3.298 0.00258 0.602
HMC_vs_SMC 5 3.835 0.000625 0.700
Metro_vs_DEMetro_Z 0 1.369 0.182 0.250
Metro_vs_DEMetro_Z 1 0.365 0.718 0.067
Metro_vs_DEMetro_Z 2 1.876 0.0708 0.342
Metro_vs_DEMetro_Z 3 2.656 0.0127 0.485
Metro_vs_DEMetro_Z 4 2.764 0.00982 0.505
Metro_vs_DEMetro_Z 5 4.614 7.41e-05 0.842
HMC_vs_Metro 0 -1.804 0.0817 -0.329
HMC_vs_Metro 1 0.134 0.894 0.025
HMC_vs_Metro 2 -3.032 0.00508 -0.554
HMC_vs_Metro 3 -3.279 0.00271 -0.599
HMC_vs_Metro 4 -4.979 2.69e-05 -0.909
HMC_vs_Metro 5 -4.762 4.91e-05 -0.869
HMC_vs_DEMetro_Z 0 -1.013 0.319 -0.185
HMC_vs_DEMetro_Z 1 0.325 0.748 0.059
HMC_vs_DEMetro_Z 2 -0.919 0.366 -0.168
HMC_vs_DEMetro_Z 3 -1.186 0.245 -0.217
HMC_vs_DEMetro_Z 4 -1.279 0.211 -0.234
HMC_vs_DEMetro_Z 5 0.588 0.561 0.107
Metro_vs_SMC 0 2.330 0.027 0.425
Metro_vs_SMC 1 2.688 0.0118 0.491
Metro_vs_SMC 2 4.164 0.000256 0.760
Metro_vs_SMC 3 3.916 0.000503 0.715
Metro_vs_SMC 4 6.114 1.17e-06 1.116
Metro_vs_SMC 5 5.979 1.69e-06 1.092
DEMetro_Z_vs_SMC 0 1.282 0.21 0.234
DEMetro_Z_vs_SMC 1 2.643 0.0131 0.482
DEMetro_Z_vs_SMC 2 2.749 0.0102 0.502
DEMetro_Z_vs_SMC 3 2.837 0.00823 0.518
DEMetro_Z_vs_SMC 4 3.423 0.00187 0.625
DEMetro_Z_vs_SMC 5 3.643 0.00105 0.665
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 3.425 7.653 14.425 -0.293
HMC 2.5 2.039 1.426 1.353 0.453
HMC 3.0 0.695 0.472 0.886 0.251
HMC 4.0 0.218 0.142 0.091 0.832
HMC 10.0 0.073 0.037 0.023 1.541
HMC 50.0 0.059 0.030 0.022 1.312
SMC 2.1 3.497 7.653 14.425 -0.288
SMC 2.5 1.096 1.426 1.353 -0.244
SMC 3.0 0.497 0.472 0.886 0.028
SMC 4.0 0.158 0.142 0.091 0.173
SMC 10.0 0.037 0.037 0.023 0.003
SMC 50.0 0.029 0.030 0.022 -0.046
Metro 2.1 4.746 7.653 14.425 -0.202
Metro 2.5 1.959 1.426 1.353 0.394
Metro 3.0 1.113 0.472 0.886 0.723
Metro 4.0 0.519 0.142 0.091 4.127
Metro 10.0 0.193 0.037 0.023 6.704
Metro 50.0 0.167 0.030 0.022 6.259
DEMetro_Z 2.1 4.294 7.653 14.425 -0.233
DEMetro_Z 2.5 1.845 1.426 1.353 0.310
DEMetro_Z 3.0 0.823 0.472 0.886 0.396
DEMetro_Z 4.0 0.281 0.142 0.091 1.522
DEMetro_Z 10.0 0.097 0.037 0.023 2.591
DEMetro_Z 50.0 0.054 0.030 0.022 1.091
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 3.639 0.000861 2.076
HMC 2.5 4.462 7.93e-05 2.587
HMC 3.0 4.251 0.000139 2.224
HMC 4.0 5.179 5.01e-06 1.955
HMC 10.0 5.186 8.26e-06 2.793
HMC 50.0 2.896 0.00606 1.264
SMC 2.1 0.432 0.668 0.151
SMC 2.5 -1.395 0.169 -0.413
SMC 3.0 0.132 0.896 0.034
SMC 4.0 0.075 0.94 0.017
SMC 10.0 -0.635 0.528 -0.161
SMC 50.0 -1.640 0.107 -0.372
Metro 2.1 11.715 1.29e-13 7.098
Metro 2.5 9.890 7.1e-11 19.774
Metro 3.0 10.653 9.27e-12 13.335
Metro 4.0 8.274 3.03e-09 11.126
Metro 10.0 9.312 2.67e-10 16.876
Metro 50.0 6.788 1.55e-07 9.077
DEMetro_Z 2.1 8.587 3.7e-11 3.122
DEMetro_Z 2.5 6.892 9.1e-08 6.139
DEMetro_Z 3.0 8.181 7.88e-10 4.225
DEMetro_Z 4.0 7.454 3.61e-09 3.185
DEMetro_Z 10.0 8.504 6.09e-10 5.443
DEMetro_Z 50.0 5.229 2.44e-06 1.363
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 6.467 4.46e-07 1.181
Metro_vs_DEMetro_Z 1 6.317 6.69e-07 1.153
Metro_vs_DEMetro_Z 2 6.890 1.43e-07 1.258
Metro_vs_DEMetro_Z 3 5.876 2.24e-06 1.073
Metro_vs_DEMetro_Z 4 6.404 5.29e-07 1.169
Metro_vs_DEMetro_Z 5 5.822 2.6e-06 1.063
DEMetro_Z_vs_SMC 0 7.328 4.51e-08 1.338
DEMetro_Z_vs_SMC 1 8.103 6.17e-09 1.479
DEMetro_Z_vs_SMC 2 8.110 6.07e-09 1.481
DEMetro_Z_vs_SMC 3 7.656 1.93e-08 1.398
DEMetro_Z_vs_SMC 4 8.812 1.07e-09 1.609
DEMetro_Z_vs_SMC 5 7.896 1.04e-08 1.442
HMC_vs_DEMetro_Z 0 -1.914 0.0656 -0.349
HMC_vs_DEMetro_Z 1 -3.551 0.00133 -0.648
HMC_vs_DEMetro_Z 2 -3.079 0.00451 -0.562
HMC_vs_DEMetro_Z 3 -2.494 0.0186 -0.455
HMC_vs_DEMetro_Z 4 -3.766 0.000752 -0.688
HMC_vs_DEMetro_Z 5 -0.239 0.812 -0.044
HMC_vs_Metro 0 -6.122 1.14e-06 -1.118
HMC_vs_Metro 1 -7.635 2.03e-08 -1.394
HMC_vs_Metro 2 -8.627 1.68e-09 -1.575
HMC_vs_Metro 3 -7.008 1.05e-07 -1.280
HMC_vs_Metro 4 -7.356 4.2e-08 -1.343
HMC_vs_Metro 5 -5.570 5.21e-06 -1.017
HMC_vs_SMC 0 3.076 0.00455 0.562
HMC_vs_SMC 1 5.059 2.15e-05 0.924
HMC_vs_SMC 2 4.551 8.82e-05 0.831
HMC_vs_SMC 3 4.949 2.92e-05 0.904
HMC_vs_SMC 4 5.473 6.82e-06 0.999
HMC_vs_SMC 5 4.030 0.000369 0.736
Metro_vs_SMC 0 11.944 1.02e-12 2.181
Metro_vs_SMC 1 10.027 6.21e-11 1.831
Metro_vs_SMC 2 10.378 2.83e-11 1.895
Metro_vs_SMC 3 8.204 4.79e-09 1.498
Metro_vs_SMC 4 9.765 1.13e-10 1.783
Metro_vs_SMC 5 6.972 1.15e-07 1.273
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.200 0.117 0.040 2.076
HMC 2.5 0.127 0.083 0.017 2.587
HMC 3.0 0.097 0.063 0.015 2.224
HMC 4.0 0.075 0.045 0.015 1.955
HMC 10.0 0.046 0.029 0.006 2.793
HMC 50.0 0.044 0.030 0.011 1.264
SMC 2.1 0.123 0.117 0.040 0.151
SMC 2.5 0.076 0.083 0.017 -0.413
SMC 3.0 0.063 0.063 0.015 0.034
SMC 4.0 0.046 0.045 0.015 0.017
SMC 10.0 0.028 0.029 0.006 -0.161
SMC 50.0 0.026 0.030 0.011 -0.372
Metro 2.1 0.401 0.117 0.040 7.098
Metro 2.5 0.419 0.083 0.017 19.774
Metro 3.0 0.269 0.063 0.015 13.335
Metro 4.0 0.214 0.045 0.015 11.126
Metro 10.0 0.134 0.029 0.006 16.876
Metro 50.0 0.128 0.030 0.011 9.077
DEMetro_Z 2.1 0.242 0.117 0.040 3.122
DEMetro_Z 2.5 0.187 0.083 0.017 6.139
DEMetro_Z 3.0 0.128 0.063 0.015 4.225
DEMetro_Z 4.0 0.093 0.045 0.015 3.185
DEMetro_Z 10.0 0.063 0.029 0.006 5.443
DEMetro_Z 50.0 0.045 0.030 0.011 1.363
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 2.396 0.023 3.700
HMC 2.5 4.143 0.00017 1.832
HMC 3.0 4.307 9.08e-05 1.676
HMC 4.0 5.334 2.24e-06 1.747
HMC 10.0 4.162 0.000154 1.761
HMC 50.0 3.167 0.00293 1.397
SMC 2.1 1.428 0.16 0.512
SMC 2.5 -0.229 0.819 -0.066
SMC 3.0 -0.342 0.733 -0.091
SMC 4.0 0.574 0.568 0.150
SMC 10.0 -0.642 0.523 -0.157
SMC 50.0 -1.956 0.0553 -0.484
Metro 2.1 10.476 1.27e-11 12.060
Metro 2.5 9.309 2.78e-10 18.688
Metro 3.0 8.543 1.54e-09 11.579
Metro 4.0 8.965 4.76e-10 10.436
Metro 10.0 7.831 9.29e-09 10.045
Metro 50.0 7.514 2.03e-08 8.736
DEMetro_Z 2.1 8.072 1.99e-09 5.132
DEMetro_Z 2.5 8.666 1.72e-10 4.369
DEMetro_Z 3.0 7.754 1.04e-09 3.114
DEMetro_Z 4.0 6.248 1.45e-07 2.441
DEMetro_Z 10.0 7.327 6.23e-09 3.246
DEMetro_Z 50.0 4.428 4.34e-05 1.214
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 7.654 1.94e-08 1.397
DEMetro_Z_vs_SMC 1 9.188 4.34e-10 1.678
DEMetro_Z_vs_SMC 2 7.663 1.89e-08 1.399
DEMetro_Z_vs_SMC 3 5.635 4.35e-06 1.029
DEMetro_Z_vs_SMC 4 7.794 1.35e-08 1.423
DEMetro_Z_vs_SMC 5 6.411 5.19e-07 1.171
HMC_vs_Metro 0 -4.028 0.000371 -0.735
HMC_vs_Metro 1 -8.170 5.23e-09 -1.492
HMC_vs_Metro 2 -7.167 6.88e-08 -1.309
HMC_vs_Metro 3 -7.804 1.32e-08 -1.425
HMC_vs_Metro 4 -5.895 2.12e-06 -1.076
HMC_vs_Metro 5 -6.126 1.13e-06 -1.119
Metro_vs_DEMetro_Z 0 5.158 1.64e-05 0.942
Metro_vs_DEMetro_Z 1 6.974 1.15e-07 1.273
Metro_vs_DEMetro_Z 2 6.353 6.08e-07 1.160
Metro_vs_DEMetro_Z 3 6.729 2.2e-07 1.228
Metro_vs_DEMetro_Z 4 5.174 1.56e-05 0.945
Metro_vs_DEMetro_Z 5 6.938 1.26e-07 1.267
HMC_vs_SMC 0 2.081 0.0463 0.380
HMC_vs_SMC 1 4.667 6.39e-05 0.852
HMC_vs_SMC 2 4.510 9.87e-05 0.823
HMC_vs_SMC 3 4.664 6.46e-05 0.851
HMC_vs_SMC 4 4.836 4e-05 0.883
HMC_vs_SMC 5 4.695 5.92e-05 0.857
Metro_vs_SMC 0 10.318 3.23e-11 1.884
Metro_vs_SMC 1 9.475 2.21e-10 1.730
Metro_vs_SMC 2 8.611 1.75e-09 1.572
Metro_vs_SMC 3 8.583 1.87e-09 1.567
Metro_vs_SMC 4 8.310 3.68e-09 1.517
Metro_vs_SMC 5 7.710 1.68e-08 1.408
HMC_vs_DEMetro_Z 0 -0.847 0.404 -0.155
HMC_vs_DEMetro_Z 1 -4.274 0.000189 -0.780
HMC_vs_DEMetro_Z 2 -2.890 0.00722 -0.528
HMC_vs_DEMetro_Z 3 -1.525 0.138 -0.278
HMC_vs_DEMetro_Z 4 -3.003 0.00546 -0.548
HMC_vs_DEMetro_Z 5 0.425 0.674 0.078
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.036 0.015 0.006 3.700
HMC 2.5 0.024 0.016 0.005 1.832
HMC 3.0 0.024 0.015 0.006 1.676
HMC 4.0 0.024 0.014 0.006 1.747
HMC 10.0 0.022 0.013 0.005 1.761
HMC 50.0 0.023 0.015 0.006 1.397
SMC 2.1 0.018 0.015 0.006 0.512
SMC 2.5 0.015 0.016 0.005 -0.066
SMC 3.0 0.015 0.015 0.006 -0.091
SMC 4.0 0.015 0.014 0.006 0.150
SMC 10.0 0.012 0.013 0.005 -0.157
SMC 50.0 0.012 0.015 0.006 -0.484
Metro 2.1 0.084 0.015 0.006 12.060
Metro 2.5 0.100 0.016 0.005 18.688
Metro 3.0 0.079 0.015 0.006 11.579
Metro 4.0 0.076 0.014 0.006 10.436
Metro 10.0 0.062 0.013 0.005 10.045
Metro 50.0 0.066 0.015 0.006 8.736
DEMetro_Z 2.1 0.044 0.015 0.006 5.132
DEMetro_Z 2.5 0.035 0.016 0.005 4.369
DEMetro_Z 3.0 0.032 0.015 0.006 3.114
DEMetro_Z 4.0 0.028 0.014 0.006 2.441
DEMetro_Z 10.0 0.029 0.013 0.005 3.246
DEMetro_Z 50.0 0.022 0.015 0.006 1.214
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Forest & Ridge Plots
Pooled
2.1 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
2.5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
4 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
50 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2.1 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
2.5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
4 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
50 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2.1
2.5
3
4
10
50
Chain
2.1
2.5
3
4
10
50

Vary_Tails_with_high_Multimodality (Mixture, nu, 30 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 7.453 2.54e-08 9.670
HMC 2.5 7.512 2.36e-08 11.991
HMC 3.0 6.325 6.31e-07 17.713
HMC 4.0 6.979 1.09e-07 21.149
HMC 10.0 9.059 5.77e-10 46.670
HMC 50.0 4.702 5.78e-05 23.689
SMC 2.1 5.992 1.44e-06 8.718
SMC 2.5 4.812 3.25e-05 3.554
SMC 3.0 5.410 5.22e-06 3.636
SMC 4.0 1.534 0.132 0.557
SMC 10.0 1.029 0.308 0.306
SMC 50.0 0.588 0.559 0.158
Metro 2.1 4.891 3.02e-05 5.443
Metro 2.5 4.700 4.05e-05 2.879
Metro 3.0 6.849 1.47e-07 14.298
Metro 4.0 7.114 7.63e-08 23.461
Metro 10.0 7.464 3.11e-08 35.842
Metro 50.0 5.692 3.68e-06 27.484
DEMetro_Z 2.1 6.899 1.31e-07 16.156
DEMetro_Z 2.5 5.843 2.39e-06 18.587
DEMetro_Z 3.0 6.004 1.55e-06 23.514
DEMetro_Z 4.0 8.102 5.91e-09 26.820
DEMetro_Z 10.0 7.136 7.31e-08 30.334
DEMetro_Z 50.0 7.998 7.8e-09 31.769
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -2.542 0.0166 -0.464
HMC_vs_DEMetro_Z 1 -1.725 0.0953 -0.315
HMC_vs_DEMetro_Z 2 -1.176 0.249 -0.215
HMC_vs_DEMetro_Z 3 -1.287 0.208 -0.235
HMC_vs_DEMetro_Z 4 2.368 0.0248 0.432
HMC_vs_DEMetro_Z 5 -1.591 0.122 -0.290
Metro_vs_SMC 0 -1.707 0.0984 -0.312
Metro_vs_SMC 1 -0.631 0.533 -0.115
Metro_vs_SMC 2 4.668 6.38e-05 0.852
Metro_vs_SMC 3 6.845 1.62e-07 1.250
Metro_vs_SMC 4 7.333 4.46e-08 1.339
Metro_vs_SMC 5 5.628 4.44e-06 1.028
Metro_vs_DEMetro_Z 0 -3.844 0.00061 -0.702
Metro_vs_DEMetro_Z 1 -5.018 2.41e-05 -0.916
Metro_vs_DEMetro_Z 2 -1.901 0.0672 -0.347
Metro_vs_DEMetro_Z 3 -0.633 0.532 -0.115
Metro_vs_DEMetro_Z 4 0.983 0.334 0.179
Metro_vs_DEMetro_Z 5 -0.793 0.434 -0.145
HMC_vs_Metro 0 2.630 0.0135 0.480
HMC_vs_Metro 1 5.550 5.51e-06 1.013
HMC_vs_Metro 2 0.945 0.353 0.173
HMC_vs_Metro 3 -0.565 0.576 -0.103
HMC_vs_Metro 4 1.728 0.0946 0.316
HMC_vs_Metro 5 -0.896 0.378 -0.164
HMC_vs_SMC 0 0.576 0.569 0.105
HMC_vs_SMC 1 4.894 3.4e-05 0.894
HMC_vs_SMC 2 5.099 1.92e-05 0.931
HMC_vs_SMC 3 6.693 2.43e-07 1.222
HMC_vs_SMC 4 9.014 6.59e-10 1.646
HMC_vs_SMC 5 4.618 7.33e-05 0.843
DEMetro_Z_vs_SMC 0 2.617 0.0139 0.478
DEMetro_Z_vs_SMC 1 4.517 9.69e-05 0.825
DEMetro_Z_vs_SMC 2 5.186 1.51e-05 0.947
DEMetro_Z_vs_SMC 3 8.080 6.54e-09 1.475
DEMetro_Z_vs_SMC 4 7.040 9.61e-08 1.285
DEMetro_Z_vs_SMC 5 7.888 1.06e-08 1.440
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.807 0.101 0.073 9.670
HMC 2.5 1.123 0.130 0.083 11.991
HMC 3.0 1.212 0.089 0.063 17.713
HMC 4.0 1.478 0.105 0.065 21.149
HMC 10.0 2.885 0.088 0.060 46.670
HMC 50.0 1.838 0.122 0.072 23.689
SMC 2.1 0.737 0.101 0.073 8.718
SMC 2.5 0.425 0.130 0.083 3.554
SMC 3.0 0.320 0.089 0.063 3.636
SMC 4.0 0.141 0.105 0.065 0.557
SMC 10.0 0.106 0.088 0.060 0.306
SMC 50.0 0.134 0.122 0.072 0.158
Metro 2.1 0.498 0.101 0.073 5.443
Metro 2.5 0.369 0.130 0.083 2.879
Metro 3.0 0.996 0.089 0.063 14.298
Metro 4.0 1.628 0.105 0.065 23.461
Metro 10.0 2.236 0.088 0.060 35.842
Metro 50.0 2.113 0.122 0.072 27.484
DEMetro_Z 2.1 1.280 0.101 0.073 16.156
DEMetro_Z 2.5 1.670 0.130 0.083 18.587
DEMetro_Z 3.0 1.580 0.089 0.063 23.514
DEMetro_Z 4.0 1.846 0.105 0.065 26.820
DEMetro_Z 10.0 1.906 0.088 0.060 30.334
DEMetro_Z 50.0 2.423 0.122 0.072 31.769
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 -1.098 0.281 -0.205
HMC 2.5 1.552 0.127 0.496
HMC 3.0 3.908 0.000492 5.500
HMC 4.0 3.819 0.000651 22.897
HMC 10.0 5.749 3.18e-06 80.948
HMC 50.0 3.706 0.000884 76.016
SMC 2.1 -1.352 0.187 -0.248
SMC 2.5 0.102 0.919 0.023
SMC 3.0 1.021 0.313 0.437
SMC 4.0 0.487 0.628 0.136
SMC 10.0 -1.844 0.0709 -0.409
SMC 50.0 -0.244 0.808 -0.063
Metro 2.1 -1.317 0.198 -0.243
Metro 2.5 0.666 0.509 0.298
Metro 3.0 3.930 0.000447 4.147
Metro 4.0 3.965 0.000439 27.501
Metro 10.0 4.449 0.000117 54.516
Metro 50.0 4.267 0.000193 85.033
DEMetro_Z 2.1 -0.933 0.358 -0.173
DEMetro_Z 2.5 3.207 0.00295 2.184
DEMetro_Z 3.0 3.591 0.00119 11.678
DEMetro_Z 4.0 4.846 3.88e-05 33.218
DEMetro_Z 10.0 4.311 0.000171 39.643
DEMetro_Z 50.0 4.547 8.91e-05 86.212
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 1.090 0.285 0.199
HMC_vs_SMC 1 1.621 0.116 0.296
HMC_vs_SMC 2 3.740 0.000806 0.683
HMC_vs_SMC 3 3.825 0.000641 0.698
HMC_vs_SMC 4 5.793 2.82e-06 1.058
HMC_vs_SMC 5 3.716 0.00086 0.678
Metro_vs_DEMetro_Z 0 -2.665 0.0125 -0.487
Metro_vs_DEMetro_Z 1 -2.313 0.028 -0.422
Metro_vs_DEMetro_Z 2 -2.127 0.042 -0.388
Metro_vs_DEMetro_Z 3 -0.542 0.592 -0.099
Metro_vs_DEMetro_Z 4 1.047 0.304 0.191
Metro_vs_DEMetro_Z 5 -0.055 0.957 -0.010
HMC_vs_Metro 0 0.923 0.364 0.169
HMC_vs_Metro 1 0.418 0.679 0.076
HMC_vs_Metro 2 0.737 0.467 0.135
HMC_vs_Metro 3 -0.529 0.601 -0.097
HMC_vs_Metro 4 1.556 0.13 0.284
HMC_vs_Metro 5 -0.565 0.576 -0.103
HMC_vs_DEMetro_Z 0 -0.693 0.494 -0.126
HMC_vs_DEMetro_Z 1 -2.283 0.0299 -0.417
HMC_vs_DEMetro_Z 2 -1.673 0.105 -0.305
HMC_vs_DEMetro_Z 3 -1.168 0.252 -0.213
HMC_vs_DEMetro_Z 4 2.310 0.0282 0.422
HMC_vs_DEMetro_Z 5 -0.458 0.651 -0.084
Metro_vs_SMC 0 0.222 0.826 0.040
Metro_vs_SMC 1 0.623 0.538 0.114
Metro_vs_SMC 2 3.606 0.00115 0.658
Metro_vs_SMC 3 3.942 0.000469 0.720
Metro_vs_SMC 4 4.478 0.000108 0.817
Metro_vs_SMC 5 4.267 0.000193 0.779
DEMetro_Z_vs_SMC 0 2.400 0.023 0.438
DEMetro_Z_vs_SMC 1 3.464 0.00168 0.632
DEMetro_Z_vs_SMC 2 3.553 0.00133 0.649
DEMetro_Z_vs_SMC 3 4.841 3.95e-05 0.884
DEMetro_Z_vs_SMC 4 4.353 0.000152 0.795
DEMetro_Z_vs_SMC 5 4.559 8.63e-05 0.832
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 6.192 13.069 33.570 -0.205
HMC 2.5 3.497 2.307 2.397 0.496
HMC 3.0 3.654 0.685 0.540 5.500
HMC 4.0 4.752 0.338 0.193 22.897
HMC 10.0 15.878 0.247 0.193 80.948
HMC 50.0 10.233 0.220 0.132 76.016
SMC 2.1 4.744 13.069 33.570 -0.248
SMC 2.5 2.363 2.307 2.397 0.023
SMC 3.0 0.920 0.685 0.540 0.437
SMC 4.0 0.365 0.338 0.193 0.136
SMC 10.0 0.168 0.247 0.193 -0.409
SMC 50.0 0.211 0.220 0.132 -0.063
Metro 2.1 4.920 13.069 33.570 -0.243
Metro 2.5 3.021 2.307 2.397 0.298
Metro 3.0 2.924 0.685 0.540 4.147
Metro 4.0 5.640 0.338 0.193 27.501
Metro 10.0 10.774 0.247 0.193 54.516
Metro 50.0 11.420 0.220 0.132 85.033
DEMetro_Z 2.1 7.275 13.069 33.570 -0.173
DEMetro_Z 2.5 7.543 2.307 2.397 2.184
DEMetro_Z 3.0 6.991 0.685 0.540 11.678
DEMetro_Z 4.0 6.742 0.338 0.193 33.218
DEMetro_Z 10.0 7.902 0.247 0.193 39.643
DEMetro_Z 50.0 11.576 0.220 0.132 86.212
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 7.522 1.95e-08 8.471
HMC 2.5 7.587 1.95e-08 12.265
HMC 3.0 6.536 3.59e-07 20.442
HMC 4.0 6.829 1.64e-07 24.047
HMC 10.0 9.137 4.81e-10 50.455
HMC 50.0 4.674 6.23e-05 23.891
SMC 2.1 8.060 4.69e-09 9.116
SMC 2.5 6.647 1.4e-07 4.620
SMC 3.0 5.962 1.14e-06 4.562
SMC 4.0 1.900 0.0641 0.751
SMC 10.0 1.056 0.296 0.316
SMC 50.0 0.466 0.643 0.123
Metro 2.1 5.380 7.11e-06 5.159
Metro 2.5 5.758 1.61e-06 3.413
Metro 3.0 6.941 1.18e-07 17.512
Metro 4.0 7.555 2.42e-08 26.307
Metro 10.0 7.361 4.08e-08 38.789
Metro 50.0 5.714 3.46e-06 28.491
DEMetro_Z 2.1 7.537 2.34e-08 14.719
DEMetro_Z 2.5 6.184 9.34e-07 18.810
DEMetro_Z 3.0 6.067 1.31e-06 28.851
DEMetro_Z 4.0 7.796 1.31e-08 30.911
DEMetro_Z 10.0 7.309 4.64e-08 32.869
DEMetro_Z 50.0 7.847 1.15e-08 32.898
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -4.237 0.00021 -0.773
Metro_vs_DEMetro_Z 1 -5.058 2.16e-05 -0.924
Metro_vs_DEMetro_Z 2 -1.955 0.0602 -0.357
Metro_vs_DEMetro_Z 3 -0.761 0.453 -0.139
Metro_vs_DEMetro_Z 4 0.983 0.334 0.179
Metro_vs_DEMetro_Z 5 -0.767 0.449 -0.140
DEMetro_Z_vs_SMC 0 2.352 0.0257 0.429
DEMetro_Z_vs_SMC 1 4.628 7.13e-05 0.845
DEMetro_Z_vs_SMC 2 5.211 1.41e-05 0.951
DEMetro_Z_vs_SMC 3 7.754 1.5e-08 1.416
DEMetro_Z_vs_SMC 4 7.208 6.18e-08 1.316
DEMetro_Z_vs_SMC 5 7.774 1.42e-08 1.419
HMC_vs_DEMetro_Z 0 -2.912 0.00684 -0.532
HMC_vs_DEMetro_Z 1 -1.763 0.0884 -0.322
HMC_vs_DEMetro_Z 2 -1.451 0.158 -0.265
HMC_vs_DEMetro_Z 3 -1.311 0.2 -0.239
HMC_vs_DEMetro_Z 4 2.436 0.0212 0.445
HMC_vs_DEMetro_Z 5 -1.698 0.1 -0.310
HMC_vs_Metro 0 2.584 0.0151 0.472
HMC_vs_Metro 1 5.330 1.01e-05 0.973
HMC_vs_Metro 2 0.711 0.483 0.130
HMC_vs_Metro 3 -0.506 0.617 -0.092
HMC_vs_Metro 4 1.686 0.102 0.308
HMC_vs_Metro 5 -1.054 0.3 -0.192
HMC_vs_SMC 0 -0.493 0.626 -0.090
HMC_vs_SMC 1 4.459 0.000114 0.814
HMC_vs_SMC 2 5.173 1.57e-05 0.945
HMC_vs_SMC 3 6.544 3.63e-07 1.195
HMC_vs_SMC 4 9.115 5.17e-10 1.664
HMC_vs_SMC 5 4.606 7.57e-05 0.841
Metro_vs_SMC 0 -2.499 0.0184 -0.456
Metro_vs_SMC 1 -1.188 0.245 -0.217
Metro_vs_SMC 2 4.761 4.93e-05 0.869
Metro_vs_SMC 3 7.160 7e-08 1.307
Metro_vs_SMC 4 7.241 5.67e-08 1.322
Metro_vs_SMC 5 5.670 3.95e-06 1.035
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.814 0.179 0.075 8.471
HMC 2.5 1.077 0.180 0.073 12.265
HMC 3.0 1.085 0.123 0.047 20.442
HMC 4.0 1.345 0.127 0.051 24.047
HMC 10.0 2.598 0.101 0.049 50.455
HMC 50.0 1.624 0.126 0.063 23.891
SMC 2.1 0.862 0.179 0.075 9.116
SMC 2.5 0.518 0.180 0.073 4.620
SMC 3.0 0.338 0.123 0.047 4.562
SMC 4.0 0.165 0.127 0.051 0.751
SMC 10.0 0.117 0.101 0.049 0.316
SMC 50.0 0.134 0.126 0.063 0.123
Metro 2.1 0.566 0.179 0.075 5.159
Metro 2.5 0.429 0.180 0.073 3.413
Metro 3.0 0.947 0.123 0.047 17.512
Metro 4.0 1.460 0.127 0.051 26.307
Metro 10.0 2.021 0.101 0.049 38.789
Metro 50.0 1.912 0.126 0.063 28.491
DEMetro_Z 2.1 1.282 0.179 0.075 14.719
DEMetro_Z 2.5 1.556 0.180 0.073 18.810
DEMetro_Z 3.0 1.480 0.123 0.047 28.851
DEMetro_Z 4.0 1.693 0.127 0.051 30.911
DEMetro_Z 10.0 1.728 0.101 0.049 32.869
DEMetro_Z 50.0 2.188 0.126 0.063 32.898
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 7.112 6.94e-08 11.868
HMC 2.5 7.178 6.04e-08 14.065
HMC 3.0 6.103 1.17e-06 21.609
HMC 4.0 6.857 1.52e-07 24.973
HMC 10.0 9.378 2.72e-10 54.882
HMC 50.0 4.833 4.01e-05 27.274
SMC 2.1 6.012 1.43e-06 11.190
SMC 2.5 5.179 1.15e-05 4.051
SMC 3.0 5.395 5.93e-06 4.041
SMC 4.0 1.618 0.113 0.595
SMC 10.0 1.155 0.253 0.341
SMC 50.0 0.317 0.753 0.089
Metro 2.1 4.878 3.27e-05 6.615
Metro 2.5 4.425 9.7e-05 3.022
Metro 3.0 6.450 4.47e-07 17.326
Metro 4.0 7.147 7.07e-08 27.590
Metro 10.0 7.851 1.15e-08 42.274
Metro 50.0 5.852 2.37e-06 31.546
DEMetro_Z 2.1 6.845 1.56e-07 21.596
DEMetro_Z 2.5 5.683 3.76e-06 22.344
DEMetro_Z 3.0 5.755 3.1e-06 29.514
DEMetro_Z 4.0 8.078 6.37e-09 31.328
DEMetro_Z 10.0 7.351 4.18e-08 36.440
DEMetro_Z 50.0 8.531 2.07e-09 36.860
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 2.725 0.0108 0.497
DEMetro_Z_vs_SMC 1 4.508 9.93e-05 0.823
DEMetro_Z_vs_SMC 2 5.084 2.01e-05 0.928
DEMetro_Z_vs_SMC 3 8.032 7.39e-09 1.466
DEMetro_Z_vs_SMC 4 7.280 5.12e-08 1.329
DEMetro_Z_vs_SMC 5 8.442 2.66e-09 1.541
HMC_vs_Metro 0 2.648 0.013 0.483
HMC_vs_Metro 1 5.617 4.58e-06 1.025
HMC_vs_Metro 2 0.935 0.358 0.171
HMC_vs_Metro 3 -0.539 0.594 -0.098
HMC_vs_Metro 4 1.820 0.079 0.332
HMC_vs_Metro 5 -0.905 0.373 -0.165
Metro_vs_DEMetro_Z 0 -4.085 0.000317 -0.746
Metro_vs_DEMetro_Z 1 -5.014 2.44e-05 -0.915
Metro_vs_DEMetro_Z 2 -1.945 0.0615 -0.355
Metro_vs_DEMetro_Z 3 -0.599 0.554 -0.109
Metro_vs_DEMetro_Z 4 0.924 0.363 0.169
Metro_vs_DEMetro_Z 5 -0.873 0.39 -0.159
HMC_vs_SMC 0 0.327 0.746 0.060
HMC_vs_SMC 1 4.899 3.36e-05 0.894
HMC_vs_SMC 2 5.043 2.25e-05 0.921
HMC_vs_SMC 3 6.646 2.75e-07 1.213
HMC_vs_SMC 4 9.328 3.12e-10 1.703
HMC_vs_SMC 5 4.765 4.88e-05 0.870
Metro_vs_SMC 0 -1.861 0.0729 -0.340
Metro_vs_SMC 1 -0.910 0.371 -0.166
Metro_vs_SMC 2 4.525 9.47e-05 0.826
Metro_vs_SMC 3 6.893 1.42e-07 1.259
Metro_vs_SMC 4 7.727 1.61e-08 1.411
Metro_vs_SMC 5 5.807 2.71e-06 1.060
HMC_vs_DEMetro_Z 0 -2.793 0.00915 -0.510
HMC_vs_DEMetro_Z 1 -1.747 0.0912 -0.319
HMC_vs_DEMetro_Z 2 -1.233 0.228 -0.225
HMC_vs_DEMetro_Z 3 -1.226 0.23 -0.224
HMC_vs_DEMetro_Z 4 2.345 0.0261 0.428
HMC_vs_DEMetro_Z 5 -1.667 0.106 -0.304
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.081 0.010 0.006 11.868
HMC 2.5 0.121 0.014 0.008 14.065
HMC 3.0 0.134 0.010 0.006 21.609
HMC 4.0 0.171 0.012 0.006 24.973
HMC 10.0 0.327 0.010 0.006 54.882
HMC 50.0 0.207 0.013 0.007 27.274
SMC 2.1 0.077 0.010 0.006 11.190
SMC 2.5 0.044 0.014 0.008 4.051
SMC 3.0 0.033 0.010 0.006 4.041
SMC 4.0 0.015 0.012 0.006 0.595
SMC 10.0 0.012 0.010 0.006 0.341
SMC 50.0 0.014 0.013 0.007 0.089
Metro 2.1 0.049 0.010 0.006 6.615
Metro 2.5 0.037 0.014 0.008 3.022
Metro 3.0 0.110 0.010 0.006 17.326
Metro 4.0 0.187 0.012 0.006 27.590
Metro 10.0 0.254 0.010 0.006 42.274
Metro 50.0 0.237 0.013 0.007 31.546
DEMetro_Z 2.1 0.138 0.010 0.006 21.596
DEMetro_Z 2.5 0.184 0.014 0.008 22.344
DEMetro_Z 3.0 0.180 0.010 0.006 29.514
DEMetro_Z 4.0 0.211 0.012 0.006 31.328
DEMetro_Z 10.0 0.220 0.010 0.006 36.440
DEMetro_Z 50.0 0.275 0.013 0.007 36.860
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 7.196 5.61e-08 12.623
HMC 2.5 6.070 1.15e-06 8.593
HMC 3.0 6.692 2.37e-07 23.373
HMC 4.0 5.970 1.71e-06 30.188
HMC 10.0 41.725 9.92e-28 90.597
HMC 50.0 263.274 6.09e-88 76.091
SMC 2.1 5.683 3.4e-06 8.122
SMC 2.5 3.844 0.000562 3.799
SMC 3.0 3.179 0.00283 1.399
SMC 4.0 1.816 0.0748 0.521
SMC 10.0 0.036 0.972 0.009
SMC 50.0 -1.957 0.0554 -0.462
Metro 2.1 3.289 0.00258 4.967
Metro 2.5 5.533 2.71e-06 2.890
Metro 3.0 4.967 2.65e-05 9.176
Metro 4.0 5.409 8.07e-06 26.648
Metro 10.0 16.285 3.75e-16 82.290
Metro 50.0 249.087 1.14e-83 76.330
DEMetro_Z 2.1 4.919 3.1e-05 12.710
DEMetro_Z 2.5 4.716 5.49e-05 14.451
DEMetro_Z 3.0 4.250 0.000202 21.843
DEMetro_Z 4.0 6.604 3.06e-07 43.616
DEMetro_Z 10.0 9.039 6.13e-10 64.401
DEMetro_Z 50.0 13.205 8.18e-14 64.135
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -0.028 0.978 -0.005
HMC_vs_DEMetro_Z 1 -1.556 0.13 -0.284
HMC_vs_DEMetro_Z 2 0.243 0.809 0.044
HMC_vs_DEMetro_Z 3 -1.791 0.0837 -0.327
HMC_vs_DEMetro_Z 4 3.883 0.000549 0.709
HMC_vs_DEMetro_Z 5 2.469 0.0197 0.451
Metro_vs_SMC 0 -1.654 0.109 -0.302
Metro_vs_SMC 1 -0.826 0.415 -0.151
Metro_vs_SMC 2 4.181 0.000244 0.763
Metro_vs_SMC 3 5.245 1.28e-05 0.958
Metro_vs_SMC 4 16.199 4.55e-16 2.957
Metro_vs_SMC 5 256.354 3.26e-50 46.804
Metro_vs_DEMetro_Z 0 -2.585 0.015 -0.472
Metro_vs_DEMetro_Z 1 -3.768 0.000748 -0.688
Metro_vs_DEMetro_Z 2 -2.372 0.0245 -0.433
Metro_vs_DEMetro_Z 3 -2.270 0.0308 -0.414
Metro_vs_DEMetro_Z 4 1.851 0.0744 0.338
Metro_vs_DEMetro_Z 5 2.493 0.0186 0.455
HMC_vs_Metro 0 3.092 0.00437 0.564
HMC_vs_Metro 1 3.871 0.000568 0.707
HMC_vs_Metro 2 4.030 0.000369 0.736
HMC_vs_Metro 3 0.562 0.579 0.103
HMC_vs_Metro 4 1.468 0.153 0.268
HMC_vs_Metro 5 -1.451 0.158 -0.265
HMC_vs_SMC 0 2.270 0.0308 0.414
HMC_vs_SMC 1 2.766 0.00976 0.505
HMC_vs_SMC 2 6.252 8.01e-07 1.141
HMC_vs_SMC 3 5.784 2.88e-06 1.056
HMC_vs_SMC 4 41.131 2.87e-27 7.509
HMC_vs_SMC 5 273.886 4.79e-51 50.004
DEMetro_Z_vs_SMC 0 1.385 0.177 0.253
DEMetro_Z_vs_SMC 1 3.272 0.00276 0.597
DEMetro_Z_vs_SMC 2 3.931 0.000482 0.718
DEMetro_Z_vs_SMC 3 6.553 3.53e-07 1.196
DEMetro_Z_vs_SMC 4 9.047 6.09e-10 1.652
DEMetro_Z_vs_SMC 5 13.342 6.61e-14 2.436
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 1.022 0.101 0.073 12.623
HMC 2.5 0.842 0.130 0.083 8.593
HMC 3.0 1.571 0.089 0.063 23.373
HMC 4.0 2.065 0.105 0.065 30.188
HMC 10.0 5.518 0.088 0.060 90.597
HMC 50.0 5.632 0.122 0.072 76.091
SMC 2.1 0.694 0.101 0.073 8.122
SMC 2.5 0.445 0.130 0.083 3.799
SMC 3.0 0.178 0.089 0.063 1.399
SMC 4.0 0.139 0.105 0.065 0.521
SMC 10.0 0.088 0.088 0.060 0.009
SMC 50.0 0.089 0.122 0.072 -0.462
Metro 2.1 0.463 0.101 0.073 4.967
Metro 2.5 0.370 0.130 0.083 2.890
Metro 3.0 0.671 0.089 0.063 9.176
Metro 4.0 1.835 0.105 0.065 26.648
Metro 10.0 5.020 0.088 0.060 82.290
Metro 50.0 5.650 0.122 0.072 76.330
DEMetro_Z 2.1 1.028 0.101 0.073 12.710
DEMetro_Z 2.5 1.327 0.130 0.083 14.451
DEMetro_Z 3.0 1.474 0.089 0.063 21.843
DEMetro_Z 4.0 2.936 0.105 0.065 43.616
DEMetro_Z 10.0 3.948 0.088 0.060 64.401
DEMetro_Z 50.0 4.767 0.122 0.072 64.135
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 -1.087 0.285 -0.204
HMC 2.5 0.272 0.787 0.063
HMC 3.0 3.796 0.000686 9.488
HMC 4.0 4.039 0.00036 53.527
HMC 10.0 31.721 4.34e-24 225.838
HMC 50.0 1185.645 1.2e-124 341.184
SMC 2.1 -1.628 0.114 -0.298
SMC 2.5 -0.596 0.554 -0.144
SMC 3.0 0.108 0.914 0.043
SMC 4.0 0.918 0.362 0.254
SMC 10.0 -0.101 0.92 -0.024
SMC 50.0 -0.018 0.986 -0.005
Metro 2.1 -1.110 0.276 -0.206
Metro 2.5 0.620 0.539 0.317
Metro 3.0 2.582 0.0147 2.422
Metro 4.0 3.767 0.00075 45.910
Metro 10.0 14.260 1.22e-14 202.850
Metro 50.0 1165.230 5.4e-123 341.298
DEMetro_Z 2.1 -1.034 0.309 -0.193
DEMetro_Z 2.5 2.423 0.0211 1.814
DEMetro_Z 3.0 2.739 0.0104 13.994
DEMetro_Z 4.0 5.378 8.88e-06 103.706
DEMetro_Z 10.0 7.708 1.68e-08 150.997
DEMetro_Z 50.0 11.878 1.16e-12 279.115
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 2.628 0.0136 0.480
HMC_vs_SMC 1 1.015 0.318 0.185
HMC_vs_SMC 2 3.755 0.000775 0.686
HMC_vs_SMC 3 4.004 0.000396 0.731
HMC_vs_SMC 4 31.677 4.75e-24 5.783
HMC_vs_SMC 5 1168.236 2.59e-69 213.290
Metro_vs_DEMetro_Z 0 -0.268 0.79 -0.049
Metro_vs_DEMetro_Z 1 -1.647 0.11 -0.301
Metro_vs_DEMetro_Z 2 -2.275 0.0305 -0.415
Metro_vs_DEMetro_Z 3 -2.959 0.0061 -0.540
Metro_vs_DEMetro_Z 4 1.947 0.0613 0.355
Metro_vs_DEMetro_Z 5 2.643 0.0131 0.483
HMC_vs_Metro 0 0.033 0.974 0.006
HMC_vs_Metro 1 -0.488 0.629 -0.089
HMC_vs_Metro 2 2.828 0.00841 0.516
HMC_vs_Metro 3 0.451 0.655 0.082
HMC_vs_Metro 4 1.400 0.172 0.256
HMC_vs_Metro 5 -1.864 0.0725 -0.340
HMC_vs_DEMetro_Z 0 -0.199 0.843 -0.036
HMC_vs_DEMetro_Z 1 -2.306 0.0285 -0.421
HMC_vs_DEMetro_Z 2 -0.800 0.43 -0.146
HMC_vs_DEMetro_Z 3 -2.324 0.0273 -0.424
HMC_vs_DEMetro_Z 4 3.947 0.000462 0.721
HMC_vs_DEMetro_Z 5 2.639 0.0132 0.482
Metro_vs_SMC 0 3.245 0.00296 0.592
Metro_vs_SMC 1 0.940 0.355 0.172
Metro_vs_SMC 2 2.739 0.0104 0.500
Metro_vs_SMC 3 3.739 0.000808 0.683
Metro_vs_SMC 4 14.299 1.15e-14 2.611
Metro_vs_SMC 5 1119.483 8.92e-69 204.389
DEMetro_Z_vs_SMC 0 2.889 0.00724 0.527
DEMetro_Z_vs_SMC 1 2.628 0.0136 0.480
DEMetro_Z_vs_SMC 2 2.815 0.00867 0.514
DEMetro_Z_vs_SMC 3 5.350 9.59e-06 0.977
DEMetro_Z_vs_SMC 4 7.694 1.75e-08 1.405
DEMetro_Z_vs_SMC 5 11.880 1.16e-12 2.169
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 6.222 13.069 33.570 -0.204
HMC 2.5 2.459 2.307 2.397 0.063
HMC 3.0 5.808 0.685 0.540 9.488
HMC 4.0 10.657 0.338 0.193 53.527
HMC 10.0 43.857 0.247 0.193 225.838
HMC 50.0 45.161 0.220 0.132 341.184
SMC 2.1 3.060 13.069 33.570 -0.298
SMC 2.5 1.962 2.307 2.397 -0.144
SMC 3.0 0.708 0.685 0.540 0.043
SMC 4.0 0.387 0.338 0.193 0.254
SMC 10.0 0.242 0.247 0.193 -0.024
SMC 50.0 0.219 0.220 0.132 -0.005
Metro 2.1 6.168 13.069 33.570 -0.206
Metro 2.5 3.065 2.307 2.397 0.317
Metro 3.0 1.992 0.685 0.540 2.422
Metro 4.0 9.189 0.338 0.193 45.910
Metro 10.0 39.418 0.247 0.193 202.850
Metro 50.0 45.176 0.220 0.132 341.298
DEMetro_Z 2.1 6.584 13.069 33.570 -0.193
DEMetro_Z 2.5 6.654 2.307 2.397 1.814
DEMetro_Z 3.0 8.241 0.685 0.540 13.994
DEMetro_Z 4.0 20.331 0.338 0.193 103.706
DEMetro_Z 10.0 29.405 0.247 0.193 150.997
DEMetro_Z 50.0 36.985 0.220 0.132 279.115
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 7.104 6.96e-08 11.177
HMC 2.5 5.883 1.95e-06 8.505
HMC 3.0 6.837 1.62e-07 28.030
HMC 4.0 5.747 3.17e-06 34.282
HMC 10.0 36.294 6.96e-26 99.713
HMC 50.0 75.688 1.47e-36 79.582
SMC 2.1 6.388 4.43e-07 7.442
SMC 2.5 3.986 0.000387 4.421
SMC 3.0 3.702 0.000689 1.892
SMC 4.0 2.024 0.0479 0.596
SMC 10.0 0.032 0.974 0.008
SMC 50.0 -1.746 0.0866 -0.398
Metro 2.1 3.712 0.000833 4.898
Metro 2.5 6.707 6.81e-08 3.447
Metro 3.0 5.173 1.51e-05 11.727
Metro 4.0 5.331 1e-05 30.916
Metro 10.0 15.993 6.08e-16 89.147
Metro 50.0 76.419 9.82e-37 79.260
DEMetro_Z 2.1 5.170 1.53e-05 12.051
DEMetro_Z 2.5 4.988 2.57e-05 15.094
DEMetro_Z 3.0 4.407 0.000131 27.289
DEMetro_Z 4.0 6.667 2.59e-07 50.254
DEMetro_Z 10.0 8.983 7.02e-10 69.183
DEMetro_Z 50.0 13.122 9.6e-14 65.426
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -2.660 0.0126 -0.486
Metro_vs_DEMetro_Z 1 -3.806 0.000676 -0.695
Metro_vs_DEMetro_Z 2 -2.389 0.0236 -0.436
Metro_vs_DEMetro_Z 3 -2.304 0.0286 -0.421
Metro_vs_DEMetro_Z 4 1.872 0.0713 0.342
Metro_vs_DEMetro_Z 5 2.784 0.00936 0.508
DEMetro_Z_vs_SMC 0 1.591 0.122 0.291
DEMetro_Z_vs_SMC 1 3.298 0.00258 0.602
DEMetro_Z_vs_SMC 2 4.083 0.000319 0.745
DEMetro_Z_vs_SMC 3 6.606 3.06e-07 1.206
DEMetro_Z_vs_SMC 4 9.010 6.65e-10 1.645
DEMetro_Z_vs_SMC 5 13.268 7.6e-14 2.422
HMC_vs_DEMetro_Z 0 -0.305 0.763 -0.056
HMC_vs_DEMetro_Z 1 -1.753 0.0901 -0.320
HMC_vs_DEMetro_Z 2 0.098 0.922 0.018
HMC_vs_DEMetro_Z 3 -1.873 0.0712 -0.342
HMC_vs_DEMetro_Z 4 3.885 0.000547 0.709
HMC_vs_DEMetro_Z 5 2.883 0.00735 0.526
HMC_vs_Metro 0 2.854 0.00789 0.521
HMC_vs_Metro 1 3.380 0.00209 0.617
HMC_vs_Metro 2 3.986 0.000415 0.728
HMC_vs_Metro 3 0.452 0.654 0.083
HMC_vs_Metro 4 1.700 0.0999 0.310
HMC_vs_Metro 5 0.220 0.827 0.040
HMC_vs_SMC 0 2.173 0.0381 0.397
HMC_vs_SMC 1 2.211 0.0351 0.404
HMC_vs_SMC 2 6.341 6.27e-07 1.158
HMC_vs_SMC 3 5.569 5.23e-06 1.017
HMC_vs_SMC 4 35.680 1.64e-25 6.514
HMC_vs_SMC 5 76.708 4.8e-35 14.005
Metro_vs_SMC 0 -1.624 0.115 -0.296
Metro_vs_SMC 1 -0.803 0.428 -0.147
Metro_vs_SMC 2 4.308 0.000173 0.786
Metro_vs_SMC 3 5.176 1.56e-05 0.945
Metro_vs_SMC 4 15.863 7.87e-16 2.896
Metro_vs_SMC 5 78.517 2.45e-35 14.335
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 1.016 0.179 0.075 11.177
HMC 2.5 0.802 0.180 0.073 8.505
HMC 3.0 1.441 0.123 0.047 28.030
HMC 4.0 1.864 0.127 0.051 34.282
HMC 10.0 5.036 0.101 0.049 99.713
HMC 50.0 5.115 0.126 0.063 79.582
SMC 2.1 0.737 0.179 0.075 7.442
SMC 2.5 0.503 0.180 0.073 4.421
SMC 3.0 0.212 0.123 0.047 1.892
SMC 4.0 0.157 0.127 0.051 0.596
SMC 10.0 0.101 0.101 0.049 0.008
SMC 50.0 0.101 0.126 0.063 -0.398
Metro 2.1 0.546 0.179 0.075 4.898
Metro 2.5 0.432 0.180 0.073 3.447
Metro 3.0 0.675 0.123 0.047 11.727
Metro 4.0 1.693 0.127 0.051 30.916
Metro 10.0 4.513 0.101 0.049 89.147
Metro 50.0 5.095 0.126 0.063 79.260
DEMetro_Z 2.1 1.082 0.179 0.075 12.051
DEMetro_Z 2.5 1.284 0.180 0.073 15.094
DEMetro_Z 3.0 1.407 0.123 0.047 27.289
DEMetro_Z 4.0 2.673 0.127 0.051 50.254
DEMetro_Z 10.0 3.525 0.101 0.049 69.183
DEMetro_Z 50.0 4.228 0.126 0.063 65.426
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 6.698 2.25e-07 15.937
HMC 2.5 5.800 2.54e-06 9.859
HMC 3.0 6.414 5.07e-07 28.675
HMC 4.0 5.970 1.72e-06 34.942
HMC 10.0 42.393 7.14e-28 102.742
HMC 50.0 157.757 4.12e-53 85.444
SMC 2.1 5.493 6.07e-06 10.184
SMC 2.5 3.431 0.00176 4.359
SMC 3.0 3.160 0.00306 1.514
SMC 4.0 1.748 0.086 0.499
SMC 10.0 -0.040 0.968 -0.011
SMC 50.0 -1.659 0.103 -0.389
Metro 2.1 2.992 0.00555 6.163
Metro 2.5 5.799 1.28e-06 3.185
Metro 3.0 4.545 8.75e-05 10.635
Metro 4.0 5.451 7.21e-06 30.249
Metro 10.0 16.436 2.97e-16 94.154
Metro 50.0 149.271 2.78e-51 85.312
DEMetro_Z 2.1 4.567 8.34e-05 16.691
DEMetro_Z 2.5 4.659 6.47e-05 17.391
DEMetro_Z 3.0 4.205 0.000228 26.726
DEMetro_Z 4.0 6.767 1.97e-07 49.829
DEMetro_Z 10.0 9.129 4.96e-10 73.725
DEMetro_Z 50.0 13.411 5.59e-14 71.480
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 1.413 0.168 0.258
DEMetro_Z_vs_SMC 1 3.272 0.00276 0.597
DEMetro_Z_vs_SMC 2 3.942 0.000468 0.720
DEMetro_Z_vs_SMC 3 6.709 2.33e-07 1.225
DEMetro_Z_vs_SMC 4 9.151 4.74e-10 1.671
DEMetro_Z_vs_SMC 5 13.477 5.14e-14 2.461
HMC_vs_Metro 0 2.922 0.00667 0.534
HMC_vs_Metro 1 3.879 0.000556 0.708
HMC_vs_Metro 2 4.069 0.000332 0.743
HMC_vs_Metro 3 0.652 0.52 0.119
HMC_vs_Metro 4 1.325 0.195 0.242
HMC_vs_Metro 5 0.218 0.829 0.040
Metro_vs_DEMetro_Z 0 -2.488 0.0189 -0.454
Metro_vs_DEMetro_Z 1 -3.811 0.000666 -0.696
Metro_vs_DEMetro_Z 2 -2.402 0.023 -0.438
Metro_vs_DEMetro_Z 3 -2.346 0.026 -0.428
Metro_vs_DEMetro_Z 4 1.892 0.0686 0.345
Metro_vs_DEMetro_Z 5 2.643 0.0131 0.483
HMC_vs_SMC 0 2.100 0.0446 0.383
HMC_vs_SMC 1 2.512 0.0178 0.459
HMC_vs_SMC 2 6.052 1.38e-06 1.105
HMC_vs_SMC 3 5.797 2.78e-06 1.058
HMC_vs_SMC 4 42.143 1.43e-27 7.694
HMC_vs_SMC 5 154.836 7.21e-44 28.269
Metro_vs_SMC 0 -1.599 0.121 -0.292
Metro_vs_SMC 1 -0.867 0.393 -0.158
Metro_vs_SMC 2 3.886 0.000545 0.709
Metro_vs_SMC 3 5.300 1.1e-05 0.968
Metro_vs_SMC 4 16.332 3.67e-16 2.982
Metro_vs_SMC 5 145.446 4.42e-43 26.555
HMC_vs_DEMetro_Z 0 -0.171 0.865 -0.031
HMC_vs_DEMetro_Z 1 -1.640 0.112 -0.299
HMC_vs_DEMetro_Z 2 0.250 0.805 0.046
HMC_vs_DEMetro_Z 3 -1.772 0.0869 -0.323
HMC_vs_DEMetro_Z 4 3.822 0.000647 0.698
HMC_vs_DEMetro_Z 5 2.586 0.015 0.472
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.105 0.010 0.006 15.937
HMC 2.5 0.089 0.014 0.008 9.859
HMC 3.0 0.175 0.010 0.006 28.675
HMC 4.0 0.234 0.012 0.006 34.942
HMC 10.0 0.603 0.010 0.006 102.742
HMC 50.0 0.619 0.013 0.007 85.444
SMC 2.1 0.071 0.010 0.006 10.184
SMC 2.5 0.047 0.014 0.008 4.359
SMC 3.0 0.019 0.010 0.006 1.514
SMC 4.0 0.015 0.012 0.006 0.499
SMC 10.0 0.010 0.010 0.006 -0.011
SMC 50.0 0.010 0.013 0.007 -0.389
Metro 2.1 0.047 0.010 0.006 6.163
Metro 2.5 0.038 0.014 0.008 3.185
Metro 3.0 0.071 0.010 0.006 10.635
Metro 4.0 0.204 0.012 0.006 30.249
Metro 10.0 0.554 0.010 0.006 94.154
Metro 50.0 0.618 0.013 0.007 85.312
DEMetro_Z 2.1 0.109 0.010 0.006 16.691
DEMetro_Z 2.5 0.146 0.014 0.008 17.391
DEMetro_Z 3.0 0.164 0.010 0.006 26.726
DEMetro_Z 4.0 0.329 0.012 0.006 49.829
DEMetro_Z 10.0 0.436 0.010 0.006 73.725
DEMetro_Z 50.0 0.520 0.013 0.007 71.480
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Mode Transitions (scatter)
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Forest & Ridge Plots
Pooled
2.1 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
2.5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
4 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
50 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2.1 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
2.5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
4 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
50 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2.1
2.5
3
4
10
50
Chain
2.1
2.5
3
4
10
50